Preheat the oven to 425 degrees F.
On a baking sheet, toss together 2 tablespoons olive oil, the beets, thyme, and a good pinch of salt + pepper. Transfer to the oven and roast for 25-30 minutes or until the beets are tender and lightly charred.
Meanwhile, bring a large pot of salted water to a boil. Boil the pasta until al dente according to package directions. Just before draining, reserve 1 cup of the pasta cooking water. Drain.
Melt the butter and 2 tablespoons olive oil in a large skillet over high heat. Add the mushrooms and cook until they just begin to caramelize on the edges, about 5 minutes. Add the garlic and cook 30 seconds to 1 minute or until fragrant. Remove the mushrooms and garlic from the skillet and place on a plate. To the same skillet, add the balsamic vinegar, honey and crushed red pepper flakes. Bring to a boil over medium high heat and cook for 5-8 minutes or until the balsamic reduces by about 1/3 and is sticky to touch. Reduce the heat to low and stir in the pasta and mushrooms. Toss to coat, if the sauce seems too thick, thin it with a little of the pasta cooking water. Season to taste with salt and pepper.
Serve the pasta immediately, topped with roasted beets, goat cheese, and pomegranate arils (if using). Eat!