Using your hands, gently mix beef with salt, pepper, allspice, and parsley. Form meat into 4 patties, slightly concave in center and slightly wider than bun (they will shrink up). Chill patties.
Cut Camembert into 1⁄4-in. slices, then halve slices crosswise.
Meanwhile, heat a grill to high (500° to 550°). Set a medium cast-iron skillet on grill and add 1 tbsp. butter and 1/2 tbsp. oil; when butter melts, add onions. Stir, season lightly with salt, cover, and cook until onions soften and turn golden, 5 to 8 minutes, stirring every couple of minutes. Scoop onions into a bowl.
Add another 1 tbsp. butter and 1/2 tbsp. oil to skillet, then add apples. Cook, covered, until golden, about 3 minutes. Stir and cook until tender throughout, about 8 minutes more. Remove pan from heat, season lightly with salt, and set aside.
Reduce heat to medium-high (400° to 450°). Grill burgers until browned, about 4 minutes. Turn and cook 2 minutes more, then top each with 2 or 3 slices cheese, cover grill, and let melt 1-2 minutes. Transfer to a baking sheet.
Toast buns, cut side down, about 2 minutes. Transfer to another baking sheet.
Assemble burgers: Slather bottom sides of buns with mayonnaise if you like. Divide apples among bottom halves of buns. Top with burgers, cheese side up, then onions. Sprinkle with parsley if you like, then add bun tops.