In a large bowl, toss the diced potatoes with 1 tablespoon of olive oil, salt, and pepper. Spread them out on a baking sheet lined with parchment paper.
Roast the potatoes for 25-30 minutes, until they are golden brown and crispy.
In the meantime, prepare the stew. In a large pot or Dutch oven, heat the remaining tablespoon of olive oil over medium heat.
Add the onion and garlic and sauté until fragrant and translucent, about 5 minutes.
Add the carrots and celery and cook for another 5 minutes, until slightly softened.
Add the lentils, vegetable broth, diced tomatoes, tomato paste, smoked paprika, thyme, rosemary, salt, and pepper. Stir to combine.
Bring the mixture to a boil, then reduce the heat to low and let the stew simmer for about 20 minutes, until the lentils are tender.
Add the mushrooms and spinach or kale to the pot and stir to combine. Cook for another 5-10 minutes, until the vegetables are tender and the stew has thickened slightly.
Taste and adjust seasoning as needed.
When the potatoes are done, remove them from the oven and toss them with vegan butter (if using).
Serve the potatoes hot with a generous spoonful of the mushroom lentil stew on top.