Pat chicken dry and season with salt and pepper. Heat 1 tablespoon oil in a 12-inch non-stick skillet over medium-high heat until just smoking. Add chicken in a single later and cook, without stirring, until beginning to brown, about 1 minute. Stir chicken and continue to cook until nearly cooked through, about 2 minutes. Transfer to a bowl and keep warm.

Add 1 tablespoon oil to now-empty skillet and heat over medium heat until shimmering. Add onion and 1/2 teaspoon salt and cook until softened, about 5-7 minutes. Stir in garlic, pepper flakes and oregano and cook until fragrant, 30 seconds. Stir in wine and simmer until nearly evaporated, 1-2 minutes. Stir in water, broth and penne. Increase heat to medium-high and cook at a simmer, stirring often, until penne is nearly tender, about 12 minutes.

Stir in broccoli and cook until penne and broccoli are tender and sauce has thickened, 3-5 minutes. Stir in chicken, along with any accumulated juices and cook until warmed through, about 1 minute. Off heat, stir in Parmesan cheese. Season with salt and pepper to taste. Serve immediately.