Sift through the lentils to remove any debris or pebbles. Then place them in a fine-mesh sieve and rinse under cold water until the water runs clear.
To make the lentils in the Instant Pot, combine all of the Lentils ingredients in the inner pot and stir to combine. Select the Pressure Cook setting (or Manual setting, depending on your model) at high pressure for a cook time of 6 minutes. Allow a natural pressure release.
To make the lentils on the stovetop, add the lentils to a large saucepan or Dutch oven and add the 2 cups of vegetable broth or water. Add the remaining ingredients (thyme, rosemary, bay leaf, 1/4 teaspoon salt, and black peppercorns). Bring the water a boil over high heat, then reduce the heat to medium and add a pinch of salt. Simmer the lentils for 20-25 minutes until just tender.
While the lentils are cooking, prepare the ingredients for the mushroom sauce (chop the vegetables, measure out the ingredients, etc.).
To make the mushroom sauce, heat a Dutch oven or large soup pot over medium heat and add the olive oil. Once the oil is shimmering, add the onion and cook until lightly browned, about 5-7 minutes, stirring frequently. While this is happening, begin boiling a separate pot of water to cook the pasta.
Add the sliced cremini and shiitake mushrooms and let them sit undisturbed for 3 minutes to allow them to brown. Then stir the mushrooms, and add a generous amount of kosher salt and pepper. Add the garlic, rosemary leaves, and crushed red pepper flakes, and stir to combine until the mixture is fragrant, about 1-2 minutes.
Pour in the white wine and deglaze the pan for 2-3 minutes, scraping up any browned bits as needed. Then add the miso paste, tahini and tamari and stir into the mushrooms to coat them. Add the cooked and drained lentils, 2 cups vegetable broth, and lite coconut milk. Stir well, and bring the stew to a boil.
Once the sauce is boiling, use an immersion blender to partially blend the sauce.Begin cooking the pasta. Once the sauce has been blended, add in the sliced kale. Bring the sauce to a boil until it is thick and creamy and the kale has wilted. Taste for seasonings and adjust accordingly.