Burgers:

• In a large nonstick skillet, heat 2 Tbs. of the oil over medium-high heat until shimmering. Add the eggplant and sprinkle with 1/2 tsp. salt and 1/4 tsp. pepper. Cook, stirring often, until the eggplant is softened and browned in spots, 6 to 8 minutes. Transfer the eggplant to a large bowl and let cool to room temperature. Add the kale, farro, breadcrumbs, garlic, Parmesan, eggs, 1/4 tsp. salt, and 1 Tbs. olive oil, until the mixture is completely combined.
• Form the mixture into four 1/2-inch-thick patties, pressing firmly to make sure they are densely packed. Cover and refrigerate the patties for 30 minutes.
• Heat the remaining 2 Tbs. olive oil in a large nonstick or cast-iron skillet over medium-high heat. Add the burgers and cook until golden brown, 2 to 3 minutes on each side.
• Transfer the burgers to a plate.

Cheese spread:

• Meanwhile, in a small skillet, heat 1 Tbs. olive oil over medium-high heat. Add the oregano leaves and cook, stirring often, until crispy and golden brown in some spots, 30 seconds to 1 minute. Transfer to a paper-towel-lined plate. In a small bowl, mix the goat cheese, crispy oregano, and a generous pinch each of salt and pepper.

Serve:

• Arrange the arugula and tomatoes on individual serving plates. Top each with a burger and serve with the goat cheese spread.