In a medium skillet over medium-low heat, melt one tablespoon of the butter. Add the orzo and toss to coat. Stir continuously until the pasta is a light golden brown.
Pour in the chicken broth and bring to a low boil. Once boiling, reduce the heat to low, cover, and simmer until most of the liquid is absorbed into the pasta, about 12 to 15 minutes.
While the orzo is cooking, melt the remaining butter in a separate large skillet over medium heat. Once melted, add the diced onion and sliced mushrooms. Cook, stirring occasionally, until the onions are softened and the mushrooms are slightly tender, about 5 to 8 minutes. Add the garlic and cook for one more minute.
Add the heavy whipping cream, parmesan cheese, kosher salt, black pepper, and red pepper flakes. Stir to combine. Cook, stirring occasionally, for 1 to 2 minutes, or until the cheese is fully melted.
Add the cooked orzo to the cream mixture and stir to combine.
Garnish with chopped parsley and more grated parmesan cheese. Serve warm.