In a medium size frying pan, heat 1 tablespoon of olive oil over medium heat. Add onions and carrots, and cook until they begin to soften (about 3 minutes). Stir in red pepper flakes and lentils, and cook for 1 minute. Stir in broth, water and salt, and bring to a boil. Reduce heat to medium-low and simmer, uncovered, until lentils are just tender and the liquid is absorbed, for about 22 to 24 minutes. Stir in spinach during last minute of cooking.
Remove pan from heat and let cool the mixture for 10 minutes. Stir in bread crumbs and egg. (Add up to 2 tablespoons (30 ml) water, if the mixture is too dry.)
For the sauce, stir Greek yogurt, feta, garlic and dill together in a small bowl. Set aside.
Heat the remaining 1 tablespoon (15 ml) of oil in a large pan over medium heat. Scoop heaping 1/2-cup portions of lentil mixture and form into 1-inch-thick patties. Add to pan and cook until golden, about 3 to 4 minutes. Flip and continue cooking for 3 minutes.
Serve on burgers buns, topped with sauce and add your favorite toppings!
