Boil the pasta: Cook the bowtie pasta in a large pot of salted boiling water until just al dente, about 10 minutes. Drain and set aside, reserving a splash of pasta water.
Season the chicken: Pat the chicken pieces dry and season generously with salt and pepper. This helps the outside sear instead of steam in the next step.
Sear the chicken: Heat olive oil in a large skillet over medium-high heat and cook the chicken in a single layer until golden and cooked through, about 6-7 minutes. Remove and set aside.
Steam the broccoli: Add the broccoli florets to the same skillet with a splash of water, cover, and steam until bright green and just tender, about 3 minutes. Transfer to the plate with the chicken.
Melt the butter: Lower the heat to medium and melt the butter in the skillet. Swirl it gently so it melts evenly without browning.
Cook the garlic: Add the minced garlic and cook until fragrant and pale gold, about 60 seconds. Stir constantly so it doesn't darken or turn bitter.
Build the sauce: Whisk in the Dijon mustard, smoked paprika, cayenne pepper, lemon juice, and lemon zest. Pour in the chicken broth and simmer for 2 minutes until the sauce turns glossy.
Combine everything: Return the chicken, broccoli, and drained pasta to the skillet. Toss gently so everything is coated in the lemon butter sauce.
Add parmesan: Sprinkle in the grated parmesan cheese and toss off the heat until it melts smoothly into the sauce. Add a splash of reserved pasta water if the sauce looks too thick.
Finish and serve: Scatter the chopped parsley over the top and give the skillet one more toss. Spoon into bowls while the sauce is still glossy.