Season chicken thighs on both sides with salt and black pepper. Rub in with your hand. Set aside.
Place 1 tablespoon butter or olive oil into a large skillet.
Place on stovetop over medium heat.
Heat until butter is melted and hot (do not brown) or olive oil is hot and shimmering.
Place 4 prepared thighs into the skillet.
Brown chicken, about 3 minutes per side. Remove to a platter.
Repeat process with remaining butter or olive oil and chicken thighs. Add browned chicken thighs to the platter with the first batch.
Deglaze skillet by adding chicken broth and gently scraping the bottom with a spatula to incorporate the flavorful brown bits into the liquid. Remove from heat.
Pour deglazing liquid into a heat-proof bowl or measuring cup. Set aside.
Place garlic, onion, carrots and potatoes into a 6-quart or larger slow cooker and spread across the bottom.
Arrange browned chicken thighs on top in a single layer as much as possible. Stack a bit if neccesary.
Spread 2/3 of the lemon slices over the chicken.
Slowly pour reserved chicken broth from the skillet (deglazing liquid) over top.
Sprinkle with the crushed rosemary leaves.
Season with additional salt and black pepper, if desired.
Cover and cook on high for 3 hours or low for 6 hours.
When cook time is complete, discard lemon slices.
Serve immediately with chopped fresh parsley and the remaining (uncooked) lemon slices cut into small wedges for garnish.