Cook pasta according to package directions and drain.
Steam the broccoli until it is crisp-tender. Set aside.
Preheat oven to 400.
Drizzle shrimp with olive oil and season with salt and pepper and place on a rack. Cook for 7-8 minutes. Remove from oven and set aside.
In a skillet or large pan over medium heat, combine the butter, garlic, cream and milk.
Cook just until ready to boil and remove from heat.
Temper the egg yolks by taking a few spoons of liquid from pan and whisking into egg yolk to raise temperature without scrambling the eggs.
Add tempered egg yolk and Parmesan to pan and whisk to incorporate.
If the sauce is too thick, add a little more milk and heat for a few more minutes.
Add in pasta and gently toss to combine.
Gently toss the pasta with the shrimp and broccoli
Add salt and pepper to taste.
Garnish with additional Parmesan and parsley.