Disney says

Cherish a Jolly Breakfast, Lunch or Dinner

Sit on the expansive Victorian-style garden patio and nibble on an assortment of sweet and flaky baked goods and desserts. Take in the prime views of people enjoying their day at the Happiest Place on Earth with Sleeping Beauty Castle and Matterhorn Bobsleds in the background.

Feel especially merry when you sample breakfast entrees like an egg and bacon croissant sandwich or a yogurt parfait. Try lunch and dinner delights like oven-roasted turkey on ciabatta, a toasted cheese sandwich or the fabulous Jolly Holiday Salad.
Friendliest.app says
The Jolly Holiday Bakery Cafe can substitute their allergy-friendly bun on nearly all sandwiches. The bun is free of gluten/wheat, milk, fish, shellfish, peanuts, tree nuts and soy. It does contain eggs.

The Jolly Holiday Bakery Cafe utilizes a separate fryer for their house-made chips to reduce cross contamination. The fryer oil contains soy.

When the Friendliest.app has eaten at the Jolly Holiday Bakery Cafe, we have been impressed with their preparation and protocols. We received a consultation from a chef who informed us that only the chefs handle allergy orders (chef's where a different color hat than the rest of the cast members) and that they are served from a separate window at the counter.

If our order is served from a window other than our designated one or is handled by anyone other than a chef, we were instructed to reject it and ask that it be remade. 

Allergy-friendly meals at Jolly Holiday Bakery Cafe