Sauté the Garlic
Heat the olive oil in a medium pot over medium heat.
Add the minced garlic and cook until fragrant but not browned, about 30 seconds.
Add the Beans and Broth
Stir in the cannellini beans and pour in the vegetable or chicken broth.
Bring the mixture to a gentle simmer.
Mash the Beans
Use a masher or wooden spoon to mash about 1/4 of the beans directly in the pot. This will help create a creamy texture.
Cook the Broccoli
Add the frozen broccoli to the pot, stir to combine, and cover with a lid.
Cook, stirring occasionally, for 3 to 6 minutes, or until the broccoli is tender.
Melt the Cheese
Reduce the heat to low and stir in half of the grated cheddar cheese until melted.
Add the remaining cheese and stir until creamy and fully incorporated.
Season and Serve
Add kosher salt and freshly ground black pepper to taste.
Serve immediately, garnished with extra cheese if desired.