Preheat the oven to 425°F (220°C). Line a rimmed baking sheet with parchment. A hot oven and a rimmed sheet will give the broccoli and tomatoes direct dry heat so they roast (caramelize) rather than steam—this concentrates flavor and adds a sweet, slightly charred note.

Prep vegetables: cut broccoli into even florets (about 2-cm pieces) so they cook evenly. Halve the cherry tomatoes. If using the potato, dice into 1/2-inch cubes and toss on a separate small sheet or the same sheet edge with 1 tablespoon olive oil, 1/4 teaspoon salt and black pepper. Spread vegetables in a single layer so they roast rather than steam.

Roast broccoli, potatoes (if using) and cherry tomatoes: toss broccoli with 1 tablespoon olive oil, 1/2 teaspoon salt and a grind of black pepper and spread on the baking sheet. Roast for 18–22 minutes, tossing once halfway through; add the cherry tomatoes during the last 10–12 minutes so they blister and release juices without turning to mush. Roasting concentrates sweetness and adds texture contrast to the creamy pasta.

While the vegetables roast, bring a large pot of salted water to a boil for the pasta. Salt the water generously (it should taste like seawater) so the pasta itself is seasoned. Cook the pasta 1–2 minutes less than package directions for al dente because it will finish cooking briefly in the sauce.

Butterfly the chicken breasts (or pound to 1/2-inch thickness for even cooking). Pat dry and season both sides with 1 teaspoon salt and 1/4 teaspoon black pepper. Dry meat sears better: patting removes surface moisture so you get a golden crust that locks juices in.

Heat a large skillet over medium-high heat and add 1 tablespoon olive oil plus 1 tablespoon butter. When the fat is shimmering and butter stops foaming, add the chicken. Sear without moving for 3–4 minutes to form a golden crust; flip and cook 3–4 minutes more until internal temperature reaches 160–165°F (71–74°C). Transfer to a cutting board to rest—resting lets juices redistribute so the meat stays moist.

To the same skillet (do not wipe it out), lower heat to medium and add the remaining 1 tablespoon butter. Add the diced onion and cook 4–5 minutes until translucent—sweating the onion releases sugars that deepen flavor. Add the minced garlic and red pepper flakes and cook 30–45 seconds until fragrant; garlic cooks fast and will turn bitter if overcooked, so short time is key.

Deglaze the pan with 1 cup chicken broth, scraping up the fond (brown bits). The fond contains concentrated flavor from the seared chicken—deglazing pulls it into the sauce. Let the broth reduce by about one-third, 2–3 minutes.

Reduce heat to low and stir in the heavy cream and lemon zest. Simmer gently (do not boil vigorously) for 3–4 minutes until the sauce slightly thickens—gentle simmer prevents the cream from breaking. Taste and adjust seasoning. Stir in 1/2 cup grated Parmesan until melted; the cheese both thickens the sauce and adds savory umami.

Drain the pasta, reserving 1 cup of the pasta cooking water. Add the pasta directly to the skillet with the sauce and toss to combine, adding reserved pasta water 1/4 cup at a time until you reach a silky clingy consistency—starchy pasta water helps emulsify and thin the sauce without diluting flavor.

Slice the rested chicken into bite-size strips and fold into the pasta along with roasted broccoli, blistered cherry tomatoes and roasted potatoes if using. Finish with lemon juice and extra grated Parmesan. The roasted vegetables add texture and concentrated flavor; folding them in at the end keeps their bright color and roast texture intact.

Serve immediately in warmed bowls and garnish with chopped parsley and a crack of black pepper. The contrast of hot silky sauce and bright roasted tomato juices makes each bite lively—present promptly so the pasta retains its perfect texture.