Bring a large pot of salted water to a boil. Add the broccoli florets and cook for 2 minutes. Remove the broccoli with a slotted spoon or sieve and plunge into an ice bath or run under cold water until cooled; set aside.

Return the same pot of water to a boil. Add the penne and cook until al dente according to package directions. Before draining, reserve ½ cup pasta water. Drain the pasta and set aside (toss with a small drizzle of olive oil if you will not add it to the sauce immediately).

Pat the chopped chicken breasts dry on the cutting board. Season with ½ teaspoon paprika, ½ teaspoon salt, and ½ teaspoon pepper; toss to coat.

Heat 2 tablespoons olive oil in a large skillet or braiser over medium-high heat. Add the seasoned chicken and cook, stirring occasionally, until golden and just cooked through; transfer the chicken to a plate with a slotted spoon and set aside.

In a liquid measuring cup or small bowl, whisk the 2 cups low-sodium chicken broth with the 2 tablespoons cornstarch until completely smooth; set aside. (If you are substituting half-and-half or evaporated milk for the heavy cream, whisk the extra 1 tablespoon cornstarch into that milk before using.)

Reduce the pan heat to medium. Add the 2 tablespoons unsalted butter to the same pan (with any browned bits and oil), then add the minced garlic and ¼ teaspoon red pepper flakes; sauté about 30 seconds until fragrant.

Whisk the broth/cornstarch mixture into the pan, then add the 2 cups heavy cream (or your chosen substitute), the very soft 2 ounces cream cheese, 1 teaspoon chicken bouillon (or Better Than Bouillon), 1 teaspoon dried basil, 1 teaspoon dried parsley, and ½ teaspoon each onion powder, dried oregano, salt, and pepper. Reduce heat to medium-low and cook, whisking often, until the cream cheese is melted and the sauce begins to thicken.

Add the 1½ cups freshly grated Parmesan a handful at a time, whisking until smooth between additions. Bring the sauce to a gentle simmer and continue to cook 3–5 minutes more, until the sauce has thickened to a creamy consistency (it will thicken further when mixed with pasta).

Stir the cooked chicken and blanched broccoli into the sauce. Add the cooked pasta and toss to coat. If the sauce becomes too thick, loosen it with reserved pasta water, a tablespoon at a time, until you reach the desired consistency.

Taste and adjust seasoning with additional freshly cracked salt and pepper if needed. Serve immediately.