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In a large pot over medium-high heat add the vegetable stock, broccoli, carrots, garlic, and onion powder. Cook about 10-15 minutes until the vegetables are tender.
Meanwhile in a smaller pot, melt the butter over medium heat. Slowly whisk in the flour. Once the vegetables are cooked, slowly mix in the flour mixture. Next, mix in the half-and-half.
Reduce the heat to low. Slowly add in the cheddar and gouda and mix until melted and well blended. Add salt and pepper to taste. Top each bowl with extra grated cheese if desired.