Heat the olive oil in a large deep skillet over medium-high heat. Season the chicken pieces with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Add to the skillet and cook, turning occasionally, until golden on the outside and cooked through (165°F internally), about 6–7 minutes. Transfer to a plate.

Reduce the heat to medium. Add the garlic and red pepper flakes to the same skillet; cook 1 minute, until fragrant and just golden — don't let the garlic brown or it turns bitter.

Pour in the chicken broth, scraping up any browned bits from the bottom of the pan. Stir in the uncooked penne. Bring to a lively simmer.

Reduce the heat to medium-low, cover, and cook until the penne is just shy of al dente, about 10 minutes. Stir once halfway through so nothing sticks. There should still be a little brothy liquid in the pan — that's your sauce base.

Uncover and stir in the heavy cream, Greek yogurt, and Parmesan until smooth and glossy. Return the chicken to the pot along with any juices. Simmer 2–3 minutes, until the sauce thickens enough to coat the penne.

Stir in the spinach a handful at a time until just wilted, about 2 minutes. Remove from heat; stir in the lemon juice, the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper, and the parsley. Serve with extra Parmesan, red pepper flakes, and lemon wedges.