Heat 2 tablespoons of butter in a large pan/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 pan and cook for 4-5 minutes per side, or until chicken is golden brown.
Remove from heat and transfer chicken to a plate. Cover and keep warm.
Reduce heat to medium and add the remaining butter and sliced shallots to the pan. Sauté shallots for 4-5 minutes, stirring occasionally, until soft and golden brown.
Add chicken stock to pan and increase heat to medium-high. Bring liquid to a boil while using a wooden spoon to scrape up brown bits from bottom of pan.
Add the rosemary and continue cooking for about 4-5 minutes until liquid is reduced by about half, stirring occasionally.
Return the chicken and its juices to the pan, 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 tender and the chicken is cooked through, and juices run clear. (Internal temperature should read 165F/75C 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!
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