Rinse the lentils: Measure the lentils into a colander or strainer. Pick over and remove any shriveled lentils or small pieces of rock or other debris. Rinse well under cool water. Drain.

Cook the lentils: Add the rinsed lentils to a medium saucepan with the vegetable broth. Bring to a rapid simmer over medium high, then reduce the heat to a very low simmer. There should be a few small bubbles, and the lentils should be barely moving. Let gently simmer for 20 to 30 minutes, until the lentils are tender. Keep an eye on them to ensure they do not dry out—you want the lentils to always be just barely covered with liquid. If the lentils are not yet tender but the liquid has been has been absorbed, add more water and continue to cook. Drain off any excess liquid and set aside.

Meanwhile, heat the olive oil in a medium skillet over medium-low heat. Once hot, add the onion and cook until onion is translucent and lightly brown, 6 to 8 minutes. Stir in the carrots and cook for another 2 minutes, then stir in the garlic and cook until fragrant, about 1 additional minute.

Place the oats and parsley in the bottom of a food processor fitted with a steel blade, then pulse a few times to begin breaking up the oats. Add the cooked lentils, onion mixture, tomato paste, oregano, salt, and pepper. Pulse a few times to start combining the mixture, then crack in the egg. Pulse a few more times until the mixture is combined but the lentils still have some texture. Set aside and let rest for 10 minutes or refrigerate overnight.

Preheat the oven to 425 degrees F. Line a large rimmed baking sheet with parchment paper, then coat the paper with nonstick spray. Roll the lentil mixture into balls that are roughly 1 1/2 inches across, about the size of a golf ball. Arrange them in a single layer on the baking sheet and mist the tops with nonstick spray. Cook for 10 minutes, then turn, mist again with nonstick spray, and continue baking 8 to 10 additional minutes, until the meatballs are browned and lightly crisp. Serve warm with pasta or vegetable noodles and your desired sauce.