in a small saucepan, add 1 tbsp butter, the diced onion, and saute over medium heat until the onion is translucent and barely browned, about 4 minutes stir intermittently
add the garlic and cook about 30 seconds, stirringconstantly so it doesn’t burn. Remove from heat and set pan aside.
in a large heavy-bottom pot add 4 tbsps. butter, flour andcook over medium heat for about 3 to 5 minutes, whisking constantly, untilflour is thickened .You are making a roux and it's very important the mixtureis thick or soup will never thicken properly later.
Slowly add the vegetable stock, whisking constantly.
SLowly add the half-and-half, whisking constantly.
Allow mixture to summer over low heat for about 15 to 20 minutes, or until it has reduced and thickened some.
Whisk intermittently to incorporate the skin that inevitablyforms, this is normal. While mixture is simmering chop the broccoli andcarrots. After simmering 15 to 20 minutes ,add the broccoli and carrots and theonion and garlic you previously set aside.
While soup simmers, grate the cheese. It's important to usea high-quality cheese because the flavor of the soup depends on it. Do not usepre-grated cheese in zip top bags because that cheese is resistant to meltingand wont incorporate well. After simmering about 20 to 25 minutes, add most ofthe cheese, reserving a small amount for garnishing bowls. Stir in the cheeseuntil melted and incorporated fully, less than 1 minutes.
Transfer soup to bowls, garnish with reserved cheese, and serve imediately. Soup will keep airtight for 5 to 7 days in the fridge. Reheat.
