Preheat oven to 400°F (200°C). In a mixing bowl, toss broccoli florets with 2 tablespoons olive oil, 1/2 cup panko breadcrumbs, and 1/2 cup grated Parmesan cheese. Spread on a parchment-lined sheet and roast for 18 minutes until edges are charred and crispy.
Boil a large pot of salted water. Cook fettuccine until al dente. Reserve 1/2 cup of pasta water, then drain.
Season chicken breasts with salt and pepper. Heat 1 tablespoon olive oil in a skillet over medium-high heat. Sear chicken for 6-7 minutes per side until internal temperature reaches 165°F. Rest for 5 minutes, then slice into strips.
To create the Spicy Feta Cream, combine feta cheese, Greek yogurt, red pepper flakes, and lemon juice in a food processor. Process until high-viscosity smooth texture is achieved. Set aside.
In a clean large skillet, melt butter over medium heat. Sauté minced garlic for 60 seconds. Add heavy cream and bring to a light simmer for 5 minutes until reduced by one-quarter.
Whisk in the remaining 1 cup of Parmesan cheese and the basil pesto into the cream mixture until emulsified. Add the cooked pasta and sliced chicken, tossing to coat. Use reserved pasta water to adjust viscosity if necessary.
Plate the pasta immediately. Top each serving with a 2-tablespoon dollop of the Spicy Feta Cream and a generous portion of the Parmesan Broccoli Crunch.