Steam carrots, onions, and garlic until fork tender. You can do this on the stove or in the microwave (I use a Lekue*). It will take about 3 minutes in the microwave and 8-10 minutes on the stove.
Add all ingredients, except pasta, to a blender and blend until smooth. Taste and add more lemon juice/salt/pepper as desired.
Cook pasta according to package instructions.
Drain the water from the pasta (keep pasta in the pot) and pour in cheese sauce. Mix until pasta is evenly coated. If your sauce is too thin, turn the stove on medium heat and cook to reduce the sauce, stirring constantly. The sauce will thicken more as the pasta cools, so don't reduce the sauce too much.