In a large pan or Dutch oven, bring salted water to a boil and cook your pasta and cook until al-dente. Drain and set aside.
To the same pot over medium heat, add the olive oil and saute the diced onion, broccoli, and carrot for 2 to 3 minutes and set aside.
Wipe down the pot and then melt the butter before adding the flour, bit by bit, and stir until evenly combined. Cook for a minute.
Slowly pour in the milk and cream and whisk until combined. Bring the mixture to a simmer and cook for about 3 to 5 minutes until thickened. Do not allow it to come to a boil.
Add the salt, pepper, onion powder, garlic powder, and dry mustard to the mixture and whisk to combine.
Add the cheese and mix until melted.
Add the pasta, onion, broccoli, and grated carrots to the cheese sauce and mix together until everything is fully coated.