Bring a large pot of salted water to a boil. Add the cauliflower and cook at a low boil until very tender, about 20 minutes. Remove the cauliflower with a slotted spoon and set aside to drain in a colander, reserving the boiling water for the pasta.
Add the fettuccine to the boiling water and cook according to the package instructions (usually about 10 minutes).
Make the sauce while the pasta cooks. In a blender, combine the cauliflower with the milk and puree until smooth.
In a large skillet over medium-low heat, heat the butter and garlic until the butter melts. Add the cauliflower puree and cook for 2 minutes. Remove the garlic. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Turn off the heat and stir in the Parmesan.
Heat a separate skillet over medium-high heat and add some olive oil. Sear the shrimp briefly on both sides until just cooked through.
Use tongs to remove the pasta from the water and transfer to the skillet with the sauce. Add 1/3 cup pasta water. Turn the heat back to medium and toss to combine until the pasta is evenly coated with the sauce. Add the shrimp and garnish with the parsley.