Season the chicken thighs: Pat the chicken thighs dry with paper towels and season both sides generously with salt and pepper. Drying the skin helps it crisp up during searing instead of steaming.
Sear until golden: Melt the butter in a large skillet over medium-high heat and add the chicken skin-side down. Sear undisturbed until deep golden, about 6 to 8 minutes per side, then transfer to a plate.
Cook turkey bacon and shallot: In the same skillet, cook the chopped turkey bacon until crisp, about 4 minutes. Add the sliced shallot and cook until softened and fragrant, about 3 more minutes.
Caramelize apple wedges: Add the apple wedges to the skillet and let them sit mostly undisturbed until the edges turn golden and slightly translucent, about 5 minutes. Stir occasionally so they color evenly without turning to mush.
Deglaze with apple cider: Pour in the apple cider, chicken broth, and apple cider vinegar, scraping up the browned bits stuck to the bottom of the pan. These bits carry most of the dish's flavor.
Simmer chicken in broth: Nestle the seared chicken thighs back into the skillet, cover, and simmer over low heat for 25 to 30 minutes. Keep the heat low enough that the liquid barely bubbles.
Check chicken temperature: Insert an instant-read thermometer into the thickest part of a thigh near the bone; it should read 165°F. If it's not there yet, cover and simmer another 5 minutes.
Remove chicken from pan: Transfer the cooked chicken to a plate and tent loosely with foil. This keeps it warm while you finish the sauce without overcooking the meat.
Thicken the sauce base: If the sauce looks thin, whisk the flour with a spoonful of the hot liquid in a small bowl, then stir it back into the skillet. Simmer 1 to 2 minutes until it loosens any lumps.
Stir in cream and mustard: Lower the heat and stir in the heavy cream and Dijon mustard. Simmer gently, uncovered, until the sauce thickens slightly and coats the back of a spoon, about 5 minutes.
Coat chicken in cream sauce: Return the chicken thighs to the skillet, spooning the apple cream sauce over the top. Let everything warm together for 2 to 3 minutes.
Rest and garnish with thyme: Remove the skillet from the heat and let the dish rest for 5 minutes so the sauce settles. Scatter fresh thyme leaves over the top before serving.