Prep the chicken and broccoli: Pat chicken dry and season well with salt, pepper, Italian seasoning, and smoked paprika. Cut broccoli into bite-size florets and rinse. Set both aside.

Heat the pan: In a large skillet, warm 1 tablespoon olive oil and 1 tablespoon butter over medium-high heat until the butter foams.

Sear the chicken: Add half the chicken in a single layer. Don’t crowd the pan. Cook 3–4 minutes per side until golden and just cooked through. Transfer to a plate and repeat with remaining chicken, adding a splash of oil if needed.

Deglaze lightly: With the heat at medium, pour in a few tablespoons of broth to loosen the browned bits. Let it reduce slightly, then pour over the chicken on the plate to save those flavors.

Cook the broccoli: Add 1 tablespoon butter to the skillet. When melted, add the broccoli with a pinch of salt and 2 tablespoons water. Cover and steam 3 minutes. Uncover and sauté 1–2 minutes more until crisp-tender and bright green. Transfer to the plate with the chicken.

Make the garlic-Parmesan sauce: Reduce heat to medium-low. Add remaining 2 tablespoons butter and the minced garlic. Cook 30–60 seconds until fragrant, not browned. Stir in remaining broth, lemon juice, and red pepper flakes. Simmer 1 minute.

Add Parmesan: Sprinkle in the Parmesan gradually, stirring until it melts into a glossy sauce. If it looks too thick, loosen with a tablespoon or two of broth or water. Taste and adjust salt and pepper.

Bring it together: Return chicken and broccoli (and any juices) to the pan. Toss to coat everything in the sauce for 1–2 minutes over low heat.

Finish and serve: Garnish with chopped parsley and a little extra Parmesan. Serve hot with rice, pasta, or crusty bread.