Firstly to the OP----
HUGE APOLOGY------ for my lateness in replying with my post trip report on the food allergy friendliness of the Pepper Market. I have been so busy since arriving home from vacation and the DIS Boards seemed like a daunting task.....partially because the end of our trip was such a disaster. Anywho, on with our experience.
We ate 3 dinners at the Pepper Market. Our first night, I told the waitress of our allergy needs and she brought out the evening chef. (on a side note--I emailed a chef at CSR before our trip regarding the allergies) I explained all my DD's allergies to eggs, peanuts, tree nuts, and soy. (banana too but that is so easy to avoid). He told me to avoid all desserts because he could not guarantee any would be safe. He said the other stations should all be fine. I asked specifically about their pasta and buns(for burgers and hot dogs) being egg and soy free because I knew my daughter would choose these options if available. He told me that ALL the pasta in their kitchen was egg free and all their buns were egg free and contained no soy flour. They did not offer to make anything special for her nor did I ask. They also did not make any special accomodations for plating but just were treated at the stations like everyone else. Fine.
The first night she had pasta shaped like ridged curly things(sorry don't know the name) with marinara sauce and italian sausage. The second trip, she had a hot dog. BTW--she also had a hot dog at Siesta's too.
The 3rd and fateful trip to the Pepper Market.....DD wanted pasta again. I told the station server what she wanted and while she was dipping the plate I noticed the noodles were VERY different. They looked like flat, wide egg noodles. I told her of our previous trip and the different noodles. He seemed puzzled saying these are the noodles they usually serve. I told him of my daughter's allergy and he was insistent that these were just like the other noodles but a different shape.
Meanwhile--my husband was getting my food. I saw they had a sign saying Chef Special was country fried steak w/gravy and mashed potatos and veggies....so just get me that.
I get back to the table with my DD's plate and I am still uneasy. I cut up the noodles and they didn't "cut" like a typical pasta noodle. I decide to taste a small piece and my DD puts a tiny bite in her mouth. I didn't think they tasted or "felt" like pasta noodles in my mouth. I told DD to spit out her mouthfull (which was not received well by a child in the spectrum). By this time our server(who was wonderful BTW) asked what was wrong, I told her what was going on and we both went back to the station. After some scrambling behind closed doors, the station server appeared and said that indeed they were egg noodles and fixed a whole new plate WITH the noodles I had descibed at the beginning of the evening with big apologies. What a mess! Thank God I had my daughter spit out the food AND she is not anaphalactic(sp?) to egg as she is with nuts.
Just to add insult to injury.........I was eating my "country fried steak" and it tasted really weird. Not just tasted bad but tasted....weird. The gravy was nasty so I scaped that off altogether but was still getting a weird taste from the "steak" so I only ate half and the veggies were good so....oh well. DH had a burrito and DD13 had pizza.
Fast forward to midnight.....food poisoning. That's right. Me and the toilet all night. We were supposed to leave that morning to fly home. Instead, poor DH was calling the airline to rebook us on a flight the following day(BIG thanks to SW---they rock!), going to the front desk to extend our stay, going back twice because they kept messing up the keys, and trying to keep the kids quiet and occupied. I ended up taking a
taxi to a walk-in clinic(because the font desk claimed there was not shuttle service to the clinic but upon arriving there--found out there definitely was--which I thought originally) because I couldn't stop the naseau and I hadn't slept since the previous night. Total nightmare but glad it was me and not my daughter.
Long story short......I would not recommend Pepper Market for people with certain food allergies that are hard to avoid....like egg or gluten or .... I think
because of the language barrier with many of the staff members and the fact that they are not Disney owned, make it much riskier for people with food allergies.
Good luck with your decision.

It really is a beautiful resort. Aside from the last night at the PM, the food there was great. The pools were fun and the bus service was easy and frequent.