Eggplant and Cabbage Dinner Frittata

Name: Eggplant and Cabbage Dinner Frittata
Ingredients: 1 Persian cucumber, thinly sliced; ½ serrano chile or 1 small jalapeño, seeds removed, sliced into rings; 1 tablespoon fresh lime juice; ½ head of Napa cabbage or 1 bunch of Tuscan kale, finely sliced, divided; 3 scallions, sliced, divided; Kosher salt; 3 tablespoons extra-virgin olive oil; 2 medium Japanese or small globe eggplants, cut crosswise into 2-inch sections, sliced into ½-inch-thick batons; 1 small onion, sliced; 2 garlic cloves, crushed; 2 large eggs; 1 ½-inch piece ginger, peeled, finely grated; 1 teaspoon tamari or soy sauce; Urfa pepper or other mild red pepper flakes (for serving)