Start by boiling a large pot of salted water. Add your pasta and cook until it's al dente according to package directions. Reserve about a cup of pasta water before draining. This starchy water can help adjust the sauce later if needed.

While the pasta cooks, bring another small pot of salted water to a simmer. Add the broccoli for about 3-4 minutes until bright green and slightly tender. It shouldn't get mushy. Remove and drain, then set aside.

In a large skillet, heat the extra-virgin olive oil over medium heat. Add the minced onion and garlic. Once they are fragrant, toss in the chicken strips. Cook until they are lightly browned and no longer pink, around 5-7 minutes.

Add the cooked pasta to the skillet with chicken and garlic. Stir in the broccoli. Next, add the sun-dried tomatoes and light cooking cream, mixing everything evenly.

Now, let’s bring in the star of the show: the pesto! Mix in the basil pesto, and adjust texture using reserved pasta water if needed. Remember, you want it creamy but not soggy. Season with salt, pepper, or red pepper flakes as desired.

Finally, plate your pasta. A generous sprinkle of freshly grated Parmesan cheese on top absolutely brings everything together. This is when it starts looking like a dish that could be served at a fancy restaurant!