Add the oil to a large pot or dutch oven and turn on the heat. Once the oil is hot, add in the chopped shallots & minced garlic and sauté for about 3 minutes until translucent.
Next, add in the chopped mushroom and carrots. Sauté everything together about 8-10 more minutes until the veggies are beginning to brown.
Once the veggies are browned, add in the lentils and spices including the cumin, paprika, turmeric, salt, and pepper. Toast everything by stirring together for about 1 minute.
Next, add in the canned coconut milk, vegetable broth, and tomato paste. Stir together and bring to a boil. Then, reduce the heat to a simmer and cook uncovered for 20-30 minutes until the lentils are cooked through. The stew will start off brothy like a soup and get thick as the lentils cook. It's important not to simmer at too high of a heat and to stir the stew every few minutes for the best results. If your lentils are taking a bit longer to cook and the stew is getting too thick, just add in a bit more veggie broth. I always start by adding in 1 ½ cups and add up to 2 cups if needed.
Once the lentils are cooked through (soft on the inside, chewy on the outside), add in the chopped kale and lime juice. Stir and cook everything together an additional 2-3 minutes.
Remove the lentil stew from the heat and serve! I like to serve over homemade mashed potatoes, but this dish is great over rice or eaten as is. Enjoy!