Heat 2 tablespoons butter in a large skillet over medium-high heat until melted. Swirl to coat bottom of pan.
Unroll chicken thighs and season each side with salt and black pepper. Add seasoned chicken to hot skillet and cook for 4-5 minutes per side, or until chicken is golden brown and releases easily from the bottom of the skillet. Remove from heat and transfer chicken to a plate. Cover and keep warm.
Reduce heat to medium and add remaining butter and sliced shallots to skillet. Sauté shallots, stirring occasionally, until soft and golden brown, approximately 4-5 minutes.
Add chicken stock to skillet and increase heat to medium-high. Bring liquid to a boil while using a spatula or wooden spoon to scrape up brown bits from bottom of pan. Add chopped rosemary leaves and continue cooking until liquid is reduced by about half, approximately 4-5 minutes, stirring occasionally.
Return chicken and its juices to the skillet, along with the frozen broccoli and thin lemon wedges. Cover and reduce heat to medium-low, and simmer for 10-12 minutes, or until broccoli is crisp tender and chicken is cooked through. (Internal temperature should read 165°F on an instant-read thermometer).
Remove from heat and serve immediately with a spoonful of pan sauce drizzled over each chicken thigh. Garnish with additional lemon wedges, if desired. Enjoy!
