Pasta with Chicken, Broccoli, and Sun-dried Tomatoes

Pasta with Chicken, Broccoli, and Sun-dried Tomatoesfrom America’s Test Kitchen 4 tablespoons unsalted butter1 pound boneless, skinless chicken breasts , trimmed of fat and cut crosswise into 1/4-inch slices1 small onion , chopped fine (about 2/3 cup)Table salt6 medium cloves garlic , minced or pressed through garlic press (about 2 tablespoons)1/4 teaspoon red pepper flakes2 teaspoons chopped fresh thyme leaves2 teaspoons all-purpose flour1 cup dry white wine2 cups low-sodium chicken broth1 bunch broccoli (about 1 1/2 pounds), florets trimmed into 1-inch pieces (about 6 cups), stems discarded1/2 pound penne pasta , ziti, cavatappi, or campanelle2 ounces grated Asiago cheese (1 cup), plus extra for serving1 jar oil-packed sun-dried tomatoes (7 to 8 1/2 ounces), rinsed, patted dry, and cut into 1/4-inch strips (about 1 cup)1 tablespoon minced fresh parsley leavesGround black pepper1 lemon , cut into wedges (optional) 1. Bring 4 quarts water to rolling boil, covered, in stockpot.2. Meanwhile, heat 1 tablespoon butter in 12-inch nonstick skillet over high heat until just beginning to brown, about 1 minute. Add chicken in single layer; cook for 1 minute without stirring, then stir chicken and continue to cook until most, but not all, of pink color has disappeared and chicken is lightly browned around the edges, about 2 minutes longer. Transfer chicken to clean bowl; set aside.3. Return skillet to high heat and add 1 tablespoon butter; add onion and 1/4 teaspoon salt and cook, stirring occasionally, until browned about edges, 2 to 3 minutes. Stir in garlic, red pepper flakes, thyme, and flour; cook, stirring constantly, until fragrant, about 30 seconds. Add wine and chicken broth; bring to simmer, then reduce heat to medium and continue to simmer, stirring occasionally, until sauce has thickened slightly and reduced to 1 1/4 cups, about 15 minutes.4. While sauce simmers, add 1 tablespoon salt and broccoli to boiling water; cook until broccoli is tender but still crisp at center, about 2 minutes. Using slotted spoon, transfer broccoli to large paper towel-lined plate. Return water to boil; stir in pasta and cook until al dente. Drain, reserving 1/2 cup pasta cooking water; return pasta to pot.5. Stir remaining 2 tablespoons butter, Asiago, sun-dried tomatoes, parsley, and chicken into sauce in skillet; cook until chicken is hot and cooked through, about 1 minute. Off heat, season to taste with pepper. Pour chicken/sauce mixture over pasta and add broccoli; toss gently to combine, adding pasta cooking water as needed to adjust sauce consistency. Serve immediately, passing additional Asiago and the lemon wedges (if using) separately.