In a large skillet, heat olive oil over medium heat. Add onions and garlic and sauté for 5 minutes, until onions are translucent and fragrant. Add the carrots and mushrooms and sauté for an additional 2 minutes, until the mushrooms have started to release their juices. Stir in spices and salt until fully coated. Add the lentils, vegetable broth, and tomato paste. Bring to a boil, reduce heat to a simmer, and cover. Cook for 30-40 minutes until the lentils are cooked all the way through and all the liquid has absorbed. Stir in the peas.