Put carrots in medium pot. Cover with water, bring to boil and cook 10 minutes. Drain, put carrots in blender and set aside. Return the pot to the stove to reuse for the cheese sauce.
Bring salted water to a boil in a large pot. Cook pasta according to package directions. Drain and set aside.
In the pot you used for the carrots, melt butter. Add flour and stir until bubbly. Add milk, a little at a time, stirring constantly. Pour mixture into blender with carrots and blend until smooth.
Return to pot and bring to a simmer. Remove from heat and add salt and cheese. Stir until cheese is melted and sauce is smooth. Pour cheese sauce over pasta and stir to combine.