In a large 5-1/2 quart saute pan over medium heat, add the olive oil. When the oil is hot and shimmery, add the onions, mushrooms, and carrots. Lightly season with salt. Saute until tender, about 15 minutes.
Move the chopped vegetables to the sides to expose the center "hot spot" of the pan and add the tomato paste. Allow the paste to sit for 2-3 minutes to caramelize. Stir to mix with the chopped vegetables.
Add the garlic and red pepper flakes and stir until fragrant, about 30 seconds. Turn off the heat to add the red wine. Return to a medium heat and deglaze the pan by scraping up any brown bits that may have accumulated on the bottom of the pan, be sure to mix it in there's lots of flavor there! Add the broth, the dry Italian seasonings, paprika, and season lightly with salt and pepper. Stir to combine.
Add the diced tomatoes (along with the juices) and stir to mix, bring the contents to a boil. Add the lentils, stir gently and let them briefly boil, about 1 minute. Reduce the heat and simmer, stirring occasionally, for approximately 30-40 minutes or until tender. Note: the lentils will absorb most of the liquid during cooking, the lentils should be tender with a subtle bite when done, be mindful not to overcook.
In the meantime, bring a large pot of water to a boil. Generously salt and add the pasta of your choice. Cook according to the package directions until about 1-minute shy of al dente, tender but firm to the bite. Reserve 1 cup of the pasta water before draining, then drain well.* Add the slightly undercooked pasta to the saute pan, along with ¼ cup of the reserved pasta water, and continue to finish cooking the pasta in the lentil mixture, 1 minute longer. Add more pasta water, about ¼ a cup at a time, if necessary.
The final consistency should be loose, with plenty of movement, but not soupy. The pasta will continue to absorb as it sits, so keep any leftover reserved pasta water on hand to loosen as desired.
Serve in pasta bowls, generously garnished with grated cheese and a light drizzle of extra virgin olive oil, if desired.
Notes
This is a great sauce to make ahead of time, whether it be a few hours, or a day or two, in advance. If making this dish ahead of time, be sure to slowly heat it through and bring it to a low boil when ready to add the pasta. * Since this dish is forgiving, don't fret if you're making the sauce and pasta simultaneously and the sauce is done before you're ready - just keep it at a very low simmer, or turn it off, while the pasta continues to cook. Turn up the heat right before you're ready to add the pasta, and don't forget to keep some pasta water handy! It's also a best practice to keep extra broth on hand, if needed. The type and brand of lentils will absorb differently, and having the extra liquid on hand during the cook time is helpful.