Preheat oven to 375°F.
Bake bacon on a slotted pan until crisp, about 18 minutes.
Heat a grill pan over medium-high heat.
Drizzle chicken or pork with olive oil and season with salt, pepper, caraway and thyme. Grill chicken or pork on 7-8 minutes, turning occasionally.
Heat a skillet over medium-high heat. Add butter and melt; add apples and sauté to tender-crisp, 5 minutes. Season with nutmeg and allspice, and deglaze with Calvados or applejack.
Combine the jam, mustard and syrup in a small bowl.
Preheat broiler with rack at center oven.
Arrange apples on roll bottoms and top with chicken or pork, bacon and cheese. Broil to melt. Slather roll tops with spread and set into place.