Soak lentils in a bowl of cold water for 1 hour. Drain and set aside.

Heat 1 tablespoon olive oil in a Dutch oven or heavy-bottomed pot over medium heat. Add onion and carrot; cook until soft, 3 to 5 minutes. Add lentils and bay leaves; stir until coated with oil.

Pour in 3 cups vegetable broth, stir, and bring to a boil. Cook at a slow boil for 10 minutes.

Reduce heat to a simmer; add buckwheat groats. Simmer until lentils are soft but not mushy and buckwheat is cooked through, about 25 minutes. Add remaining 1 ½ cups broth if needed.

Off heat, stir in spinach until wilted. Remove bay leaves.