• In a small saucepan, add 1 tablespoon butter, the diced onion, and sauté   over medium heat until the onion is translucent and barely browned, about 4 minutes. Stir intermittently.
• Add the garlic and cook about 30 seconds, stirring constantly so it doesn’t burn. Remove from heat and set pan aside.
• In a large heavy-bottom pot, add 4 tablespoons butter, flour, and cook over medium heat for about 3 to 5 minutes, whisking constantly, until flour is thickened. You are making a roux and it’s very important the mixture is 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 simmer over low heat for about 15 to 20 minutes, or until it has reduced and thickened some. Whisk intermittently to re-incorporate the ‘skin’ that inevitably forms, this is normal.
• While mixture is simmering, chop the broccoli and carrots. After simmering 15 to 20 minutes, add the broccoli, carrots, and the onion and garlic you previously set aside.
• Add the salt, pepper, optional paprika, optional dry mustard powder, and optional cayenne.  Stir to combine.
• Allow soup to simmer over low heat for about 20 to 25 minutes, or until it has reduced and thickened some. Whisk intermittently to re-incorporate the ‘skin’ that inevitably forms, this is normal.
• Optional: I used a Braun hand blender to blend the vegetables into a creamier consistency.
• While soup simmers, grate the cheese. After simmering about 20 to 25 minutes, add most of the cheese, reserving a small amount for garnishing bowls. Stir in the cheese until melted and incorporated fully, less than 1 minute.
• Transfer soup to bowls, garnish with reserved cheese, and serve immediately. Soup will keep airtight for 5 to 7 days in the fridge. Reheat gently in the microwave.

Recipe slightly adapted from Averiecooks.com