Heat olive oil in a skillet over medium heat. Cook until browned and a little crispy, about 5-6 minutes
Add the leek slices with the parsnip cubes. Add a few thyme leaves with the stem. Cook over medium heat, stirring occasionally until the leek is silky and the parsnip starts to soften and pick up some color, about 5-7 minutes
Fish out and take out the thyme stems. Add 3 minced garlic cloves and red pepper flakes to taste. Cook about a minute more
Add the rigatoni directly to the pan. Pour in the chicken broth and heavy cream. Add extra broth/cream/water to mostly cover the pasta. Stir and bring to a boil, reducing to a strong simmer. Cook uncovered, stirring frequently, until pasta is al dente and the sauce has thickened. About 10-11 minutes
Stir in Parmesan with salt and pepper to taste. Let the pasta sit a minute to have the sauce settle. Serve and enjoy!