Pulse shallots, garlic, and salt in a food processor until finely chopped, about 12 pulses. Transfer to a wide pot, and add oil. Cook, whisking often, over medium-low until shallots and garlic turn golden brown and bubbles in oil become smaller, about 11 minutes. Turn off heat; add Aleppo pepper, sugar, cumin, caraway, coriander, Urfa biber, guajillo chile, and ají panca chile to pot, and stir to combine. Let stand 10 minutes.
Carefully transfer shallot-garlic mixture to a blender, and process until peppers and seeds are roughly the same size, about 15 seconds. (Do not process too long, or you will lose the texture.) Let cool in blender until mixture is room temperature, about 1 hour. Make the cabbage marinade:
Stir together vinegar, 4 cups water, sugar, and salt in a large bowl until sugar and salt are completely dissolved. Stir in ginger, garlic, serrano chile, and dill. Let steep, uncovered, in refrigerator until flavors meld, at least 2 hours or up to 24 hours. While marinade steeps, make the steamed cabbage:
Slice each cabbage into 2 (2-inch-thick) planks. Rub salt evenly over both sides of planks.
Pour water to a depth of 1 inch into a large pot. Bring water to a boil over high. Place cabbage planks in a large steamer basket, and place steamer basket over boiling water in pot. Cover and reduce heat to medium; steam until cabbage is fork-tender, 30 to 40 minutes. Remove cabbage from steamer basket; place on a wire rack set inside a baking sheet, and let drain about 10 minutes.
Place 2 warm cabbage planks in cabbage marinade. Place a weight, such as a plate, on top of cabbage to fully submerge cabbage planks. Let stand 10 minutes. Transfer cabbage to wire rack, and let stand until dry. Repeat procedure with remaining 2 cabbage planks.
Stir together labneh and maple syrup in a medium bowl until combined. Refrigerate until ready to serve.
Preheat oven to 350°F. Working in 4 batches, heat 2 tablespoons oil in a large skillet over medium-high. Sear 1 cabbage plank until golden brown, about 5 minutes per side. (The best way to get an even sear is to place a weight, like a cast-iron skillet or burger press, on top of cabbage.) Transfer to a large rimmed baking sheet. Roast cabbage planks in preheated oven until heated through, about 10 minutes. Slice cabbage planks in half crosswise.
Spoon about ¼ cup labneh mixture onto center of each of 8 plates, and spread into a round slightly larger than cabbage plank half. For each serving, place cabbage plank half on labneh, and drizzle with 3 tablespoons caraway-chile crisp. Garnish with almonds, red onions, mint, basil, and additional dill.