Heat oil and Earth Balance in a skillet or sautéing pan over medium high heat. When hot, add onions, then garlic, be careful not to let the garlic burn. Then, mix in cumin, curry powder, and thyme. Add the carrots and stir until they are coated with the other ingredients.
Pour in broth. Add some salt and a bit of pepper. Bring to a boil, then reduce to medium heat and boil uncovered for 10-20 minutes, until broth has mostly evaporated.
After water has evaporated, allow the carrots and onions to start to caramelize by letting them cook for 10-15 minutes, flipping every 5 minutes or as necessary to prevent them sticking to the pan.