Peel and dice carrots and medium yellow onion(s). Mince cloves garlic.
Place dried red lentils in a fine-mesh strainer. Pick through the lentils, discarding any broken or discolored ones. Rinse under cool water until the water runs clear, about 1 minute. Set aside to drain while you cook the vegetables.
Heat olive oil in a large pot or Dutch oven over medium-high heat until shimmering. Add the carrots and onion and sauté until softened, about 5 minutes. Add the garlic, curry powder, ground cumin, dried thyme, and kosher salt. Cook until fragrant, about 1 minute.
Add the lentils, tomato sauce, and broth, stir to combine, and bring to a simmer. Cover and reduce the heat to maintain a gentle simmer. Cook, stirring occasionally until the lentils are tender, 18 to 22 minutes.
Remove from the heat and stir in spinach until wilted. Serve immediately.
