Bring a pot of water to a boil. Meanwhile, wash the broccoli and cut it into small florets. Peel the garlic and shallot, and finely dice them.

Once the water is boiling, reduce the heat slightly and add the broccoli. Simmer for 4 to 5 minutes. Meanwhile, fill a bowl with ice cubes and cold water. After cooking, transfer the broccoli to the ice bath for 20 to 30 seconds, then drain it in a colander.

Bring the water in the pot back to a boil, add salt, then add the pasta and cook according to the package instructions.

Meanwhile, heat the oil in a skillet. Add the garlic and shallot and sauté with a pinch of salt for about 1 minute. Add the broccoli florets and gently crush some of them with a wooden spoon. If needed, add a little pasta water to prevent the garlic from burning.

Drain the pasta, reserving a little pasta water. Add the pasta, cream cheese, pesto, and about 3–4 tbsp of the reserved pasta water to the skillet, and stir well. Mix in the Parmesan and season with salt and pepper to taste.

Optionally, finish the pasta with a little lemon zest to taste.