Place cubed potatoes in a large pot of salted water. Bring to a boil and cook for 15-20 minutes until fork-tender.
While potatoes cook, heat olive oil in a separate large pot over medium heat. Sauté onion, carrots, and celery for 6-8 minutes until softened.
Add minced garlic, tomato paste, thyme, and smoked paprika to the vegetables. Cook for 2 minutes while stirring constantly.
Pour in the rinsed lentils and vegetable broth. Bring to a boil, then reduce heat to low and simmer, covered, for 35-40 minutes until lentils are tender and liquid is mostly absorbed.
Drain the cooked potatoes and return them to the pot. Add Greek yogurt, soy milk, salt, and pepper. Mash until smooth and creamy.
Stir the nutritional yeast into the finished lentil stew to enhance protein content and savory flavor.
Divide the mashed potatoes into four bowls and ladle the thick lentil stew over the top. Garnish with fresh herbs if desired.