Heat 2 tablespoons of butter in a large skillet over medium-high heat until melted. Swirl the butter to coat the bottom of the pan.

Season both sides of the chicken thighs and add to the hot skillet. Cook for 4-5 minutes per side, or until the chicken is golden brown and releases easily from the bottom of the pan. Transfer the chicken to a plate, cover it, and keep it warm.

Reduce the heat to medium and add the remaining tablespoon of butter as well as the sliced shallots to the skillet. Saute the shallots, stirring occasionally, until soft and golden brown, about 4-5 minutes.

Add the chicken stock to the skillet and increase the heat to medium-high. Bring it to a boil, while using a spatula or wooden spoon to scrape up the brown bits from the bottom of the pan.

Add the chopped rosemary to the skillet and continue cooking until the liquid is reduced by about half, about 4-5 minutes. Stir occasionally.

Return the chicken and any accumulated juices to the pan, along with the thinly sliced lemon wedges. Cover and reduce the heat to medium-low. Simmer for 10-12 minutes or until the broccoli is crisp-tender and the chicken is cooked through (165° on an instant-read thermometer).

Remove from the heat and serve immediately with a spoonful of the pan sauce drizzled over each chicken thigh. Garnish with additional lemon wedges.