Stark äggplanta frittata

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1. 1
   Place a rack in middle of oven; preheat to 325°. Trim tops off 1 lb. Japanese eggplants (about 4 medium) and halve lengthwise; discard tops. Cut halves lengthwise into 4 strips each. Cut strips crosswise to make 3"-long pieces.
2. 2
   Heat 1 Tbsp. unsalted butter in a large nonstick skillet over medium-high. Add half of the eggplant and ¼ tsp. Diamond Crystal or Morton kosher salt. Cook, stirring occasionally with a heatproof rubber spatula, until golden brown and tender, 6–8 minutes. Transfer to a plate. Repeat with 1 Tbsp. unsalted butter, ¼ tsp. Diamond Crystal or Morton kosher salt, and remaining eggplant, leaving in pan.
3. 3
   Meanwhile, whisk 6 large eggs, ½ cup whole milk, 2 tsp. cornstarch, and remaining 1½ tsp. Diamond Crystal or ¾ tsp. Morton kosher salt in a medium bowl. Add 1 medium red onion, finely chopped, ½ bunch cilantro, finely chopped (including stems), and 1 serrano chile or jalapeño, halved, thinly sliced, and stir to combine.
4. 4
   Return all of the eggplant to skillet, add remaining 2 Tbsp. unsalted butter, and stir until melted. Pour egg mixture over eggplant, reduce heat to medium-low, and cook, scraping and stirring, until egg mixture is half set, about 5 minutes. Smooth surface and transfer pan to oven. Bake frittata until puffed and just set (it should wobble slightly in the center when gently shaken), 8–10 minutes. Let cool 5 minutes.
5. 5
   Scatter cilantro leaves with tender stems over frittata. Run a small offset spatula around sides to loosen and cut into wedges. Serve with steamed white rice or toasted bread and ketchup if desired.