Pat the chicken thighs dry, then season both sides with 1 teaspoon of Italian seasoning, along with salt and pepper to taste.
Melt the butter in a large skillet over medium-high heat. Allow the pan to get hot before adding the chicken.
Working in batches if necessary, place the chicken thighs in the hot skillet. Sear for 3-4 minutes per side, or until nicely browned. The chicken does not need to be fully cooked at this point.
Transfer the seared chicken thighs to a plate while you prepare the potatoes.
Add the red potatoes to the Crockpot along with the olive oil, minced garlic, remaining 1 teaspoon of Italian seasoning, and salt and pepper to taste. Toss until the potatoes are evenly coated, then spread them into an even layer.
Arrange the seared chicken thighs on top of the potatoes, keeping the skin side facing up.
Cover and cook on High for 3-4 hours or Low for 6-8 hours, until the potatoes are fork-tender and the chicken is fully cooked. Chicken thighs should reach a safe internal temperature of at least 165°F when checked in the thickest part without touching the bone.
Sprinkle the freshly grated Parmesan cheese over the chicken and potatoes, then garnish with chopped fresh parsley before serving.