Cook and drain the pasta according to the directions on the package. Return the drained pasta to the pot.
While the pasta is cooking, dice the broccoli, stem and all. It's all edible--don't just use the florets!
In a small saucepan, combine the half and half with the vegetable broth and bring to a boil over medium-high heat, stirring occasionally. After boiling, reduce the heat to medium and cook for 5 minutes.
Add the Gorgonzola and salt and pepper to taste. Whisk until melted and smooth.
Add the broccoli and cook it until it's as tender as you want it. If you want it really tender, you may want to steam it separately. I like my vegetables pretty raw, so I just added the broccoli to the sauce, mixed it in, and moved on.
Pour the sauce and broccoli mixture over the pasta and stir to combine evenly. Top with chopped walnuts before serving.