Step 1

Place the oats in a food processor; pulse until finely chopped, 6 to 8 times. Add the beans; pulse until chopped, about 4 times. Add the garlic powder, smoked paprika, Marmite, salt, and egg; process until well blended. Remove the blade from the processor; add the farro and stir in with a spatula (so you don’t have to use— and wash—a separate bowl).

Step 2

Heat a large nonstick skillet over medium heat. While the pan heats, pat the bean mixture into an even layer in the food processor. Score the mixture with your spatula to divide it evenly into quarters. Scrape up one quarter of the mixture at a time and shape into a bun-size patty (3 ½ to 4 inches in diameter). Place the patties on a plate or a piece of wax or parchment paper.

Step 3

Add the oil to the hot pan and swirl to coat. Add the patties to the pan; cook until browned and slightly crisp on the outside, about 3 minutes per side. Spread 1 tablespoon mayo over each side of each bun. Top the bottom half of each bun with 1 tomato slice, 1 patty, and ¼ cup potato sticks. Arrange lettuce on top bun halves. Bring buns together to assemble the burgers.

Step 4

Place the egg yolk in a mini food processor. Top with the lemon juice, Marmite, mustard, and salt; pulse until combined, 3 to 4 times. Slowly drizzle in the oil through the opening in the lid, pulsing almost constantly, until emulsified and thick. If your processor doesn’t have a hole, remove the top periodically to add the oil. Transfer to an airtight container. It will keep in the refrigerator for up to 1 week.