Step 1: Prepare the aromatics. Cut the shallot in half; roughly chop one half and mince the other. Smash one clove of garlic and mince the other. Keep these separate as they’ll be used in different parts of the recipe.
Step 2: To the bowl of a food processor fitted with an s-blade, add the rough chopped shallot, smashed garlic clove, parsley leaves, Fresno chili, cumin, ¾ tsp kosher salt, and a few grinds of black pepper. Pulse a few times to mince the shallot, garlic, parsley, and chili.
Step 3: Next, add the breadcrumbs, shredded carrot, egg, and half the lentils (you can eyeball it, or measure a generous 1½ cups) to the food processor. Process until well blended, scraping down the sides a couple of times.
Step 4: Transfer the mixture to a mixing bowl. Fold in the remaining lentils and crumbled goat cheese until well distributed. Pop the bowl into the fridge for about 10 minutes to firm up.
Step 5: Meanwhile, in a small bowl, combine the Greek yogurt, reserved minced shallot and garlic, apple cider vinegar, honey, and ¼ tsp kosher salt to make a tangy burger sauce. Stir well.
Step 6: Just before cooking, form the chilled lentil mixture into 6 equal patties.
Step 7: Heat a nonstick skillet (cast iron works well for this) over medium heat. Generously coat the bottom of the skillet with cooking spray or oil. Cook the lentil burgers for 3 to 4 minutes on each side, adding more cooking spray/oil as needed, until golden brown and heated through.
Step 8: Assemble your burgers. Spread some yogurt sauce on each bun, then build your burgers topping them with a cooked lentil patty, a slice of tomato, and a handful of fresh arugula. Serve immediately.