Bring a large pot of water to a rolling boil. Salt the water and add the spaghetti. Cook the spaghetti until al dente, about 8-10 minutes. Drain and transfer back to the pot.
While your spaghetti is cooking, prepare the cream sauce. Melt 2 tablespoons of unsalted butter in medium saucepan over medium heat. Whisk in the flour and cook for 2-3 minutes or until golden. Whisk in the vegetable broth. Bring to a boil and then reduce to a simmer. Cook until slightly thickened, about 3-4 minutes. Whisk in the heavy cream, season with salt and black pepper to taste, and cook for an additional 2 minutes or until the sauce is thickened to your liking. Whisk in 1 cup of the Pecorino cheese in 1/4 cup increments, making sure the cheese is completely melted after each addition. Remove from heat.
Pour the sauce into the pot with the pasta. Toss to coat. Serve with toasted breadcrumbs (recipe below) and an additional sprinkling of Pecorino cheese. Season with black pepper if desired.
For the breadcrumbs, heat the remaining 1 tablespoon of butter in a small saute pan over medium low heat. Once melted, add the bread crumbs. Stir frequently until lightly toasted. Season with salt and black pepper if desired. Remove from heat. Breadcrumbs will store in an airtight container for about a week.