Preheat the oven to 400 degrees F. Heat 1 tablespoon olive oil in a medium saucepan over medium heat. Add the garlic and cook, stirring, until softened, about 1 minute. Add 1 cup water, the quinoa, chicken broth, tomatoes, 1/4 teaspoon salt and a few grinds of pepper; bring to a simmer, stirring. Reduce the heat to medium low, cover and cook until the quinoa is tender and the liquid is mostly absorbed, 12 to 15 minutes. Remove from the heat and stir in the cheese and parsley. Cover to keep warm.
Meanwhile, toss the broccoli with the remaining 1 tablespoon olive oil on a baking sheet; season with salt and pepper. Add the kielbasa to the baking sheet. Roast until the broccoli starts browning and the kielbasa is hot throughout, 15 to 18 minutes. Let cool slightly, then slice the kielbasa. Serve the quinoa topped with the kielbasa, broccoli and more cheese.