Cut the stalks off 1 1/2 pounds broccoli. Cut the florets into 1- to 1 1/2-inch pieces. Trim the tough, woody ends of the stems, peel until you get to the lighter smooth parts of the stems, then slice crosswise into 1/4-inch pieces.
Place the florets and stems (7 to 8 cups) in a large bowl. Drizzle with 2 tablespoons olive oil, 1/2 teaspoon kosher salt, and 1/4 teaspoon red pepper flakes, and toss to combine.
Heat an air fryer to 390°F to 400°F. Arrange the broccoli florets and stems in an even layer in the basket or tray of a 5 1/2-quart or larger air fryer. Air fry, tossing every 5 minutes, until the broccoli is tender with brown and crispy edges, 10 to 12 minutes total.
Transfer the broccoli to a serving platter and top with finely grated Parmesan cheese or nutritional yeast if desired.