Melt 1 tablespoon of the butter in a large skillet over medium-high heat.
Season both sides of the chicken with the salt and pepper and add to the skillet.
Cook for 4-6 minutes until golden brown, then flip and cook an additional 4-5 minutes or until cooked through and no longer pink in the center. See notes for how to finish larger chicken breasts in the oven.
Remove the chicken and place on a plate. Tent with foil to keep warm.
Add the remaining butter to the skillet.
Once melted, add the garlic and shallots and cook for 1-2 minutes until translucent, scraping up any brown bits.
Pour in the chicken stock, lemon juice, lemon zest, and heavy whipping cream.
Bring to a boil until reduced by half and thickened, about 2 minutes, then reduce heat to simmer.
Place the chicken back in the pan to warm, spooning the lemon garlic sauce over it.
Garnish with the parsley and lemon slices, if desired.