4 TB salted butter
1 large onion, roughly chopped
6 garlic cloves, chopped
1 tsp tarragon
1 cup precut matchstick carrots
1 cup half & half (or heavy cream)
4 cup good quality vegetable broth
2 large bay leaves
4 TB cornstarch, dissolved in 4 TB water
5 cups frozen broccoli florets, thawed
1 tsp kosher salt, plus more as needed
½ tsp freshly ground black pepper, plus more as needed
4 cups extra sharp cheddar cheese, freshly grated and lightly packed
Optional: extra broccoli florets and grated cheese for topping, breads or crackers (GF if desired) for dipping