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1
Heat 2 tablespoons olive oil in a skillet over medium-high heat.
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2
Cook and stir diced onion with 1 teaspoon salt until onion is slightly translucent, about 5 minutes.
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3
Add eggplant, reduce heat to medium, and cook and stir until eggplant is opaque and softened, 3 to 5 minutes more.
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4
Stir garlic, 1 teaspoon black pepper, cumin, cinnamon, and oregano into eggplant mixture; cook and stir until fragrant, about 1 minute.
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5
Add tomato paste; cook and stir until heated through, about 2 minutes.
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6
Transfer mixture to a plate and cool completely.
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7
Cover plate with plastic wrap and refrigerate until chilled, at least 15 minutes.
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8
Whisk 1 1/2 tablespoons olive oil and flour together in a saucepan over medium-high heat until golden and bubbling, 2 to 3 minutes.
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9
Pour milk into butter-flour mixture, whisking constantly as it simmers and forms a smooth, thick sauce, 3 to 5 minutes.
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10
Season with nutmeg, a pinch black pepper, and a pinch cayenne pepper.
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11
Remove from heat and stir Parmesan cheese into milk mixture until melted.
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12
Combine lamb, chilled eggplant mixture, and a pinch of salt together in a bowl.
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13
Form into four patties and place on a plate.
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14
Cover the plate with plastic wrap and refrigerate until just before cooking.
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15
Place tomato slices in a shallow bowl.
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16
Season tomatoes with chopped mint, a pinch of salt, and a pinch of black pepper.
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17
Pour rice vinegar over the top and toss to coat.
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18
Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
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19
Cook burgers until slightly pink in the center, about 4 minutes per side.
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20
An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C) for medium.
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21
Spread desired amount of cheese sauce onto both sides of each hamburger bun.
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22
Place burger on bottom bun, place 2 tomato slices atop the burger, and place top half of the bun over the tomatoes.
