Soak the lentils (optional). Add the dry red lentils to a bowl, cover with water, and soak for at least 2 hours, ideally 8 hours. Once soaked, drain the soaking water and rinse the lentils.
Cook the lentils. Add the soaked (or just rinsed) lentils, water, and salt to a small pot and bring to a boil over medium heat. Reduce the heat to low, cover, and cook the lentils until all the water is absorbed, for 12-15 minutes. The lentils should be dry when they are done cooking.
Sauté the vegetables. Heat the olive oil in a medium skillet over medium-high heat. Add the onion and garlic, and sauté until translucent, for 5-7 minutes. Add the carrots and zucchini, season with salt, and sauté until the vegetables have softened, for about 5 minutes.
Mix all the ingredients. Add all the ingredients to a mixing bowl and mix to combine. You could also use a food processor, but in that case, pulse the ingredients only a few times to combine. Be careful not to purée!
Shape the patties. Using a ⅓ cup-size measuring cup, form the mixture into 10 patties.
Cook the patties. Heat a well-seasoned cast iron skillet over medium heat. Brush the skillet with a little oil and cook the lentil patties until golden brown, for about 5 minutes per side, turning the heat down as necessary. The exact timing will depend on the heat of your stove and cookware.
Serve the lentil patties in a bun or atop mixed greens with desired toppings.
Store. Leftover lentil patties keep well covered in the refrigerator for up to 5 days. For longer-term storage, freeze uncooked pre-shaped patties in an airtight container, separating each row with a piece of parchment paper, for up to 3 months. (You can freeze cooked lentil patties as well, but they are never quite as good).