Place the eggplant quarters onto a plate and salt them generously. Let stand for 5 to 10 minutes to draw out some of the moisture, then pat them dry with a paper towel.

In a large skillet, heat the oil over medium-high heat until it’s very hot and rippling. Add half the eggplant quarters, cut-side down, and cook until browned nicely on the bottom, 2 to 3 minutes. Turn and cook on the second cut side until nicely browned, 2 to 3 minutes more. Transfer to a plate and repeat with the remaining eggplant quarters.

Place the shiitakes in a large bowl. Drizzle with the remaining 2 to 3 tablespoons olive oil and the soy sauce, and season generously with salt. Toss well to coat, then dump the shiitakes onto the prepared baking sheet and arrange in a single layer. Bake for 15 to 20 minutes, stirring them halfway through the cooking time, until the shiitakes are a deep rich brown and crisped through.

Add a bit more oil to the skillet as needed, then add the onion and jalapeño and cook over medium heat until they are barely softened and have become very fragrant, 4 to 5 minutes. Stir in the coconut milk, ginger, curry paste, peanut butter, sambal oelek, and a generous pinch of salt. Bring to a simmer, then return the seared eggplant quarters to the skillet and use a spoon to coat them with the sauce. Reduce the heat to medium-low and simmer, stirring every 5 minutes or so, until the eggplant is tender and fully cooked but not falling apart and mushy, 20 to 30 minutes. The sauce should be the consistency of buttermilk—thick enough to coat everything but not so thick that it’s gloppy. If it gets too thick, add a touch of water to loosen it up.

Just before serving, sprinkle the cilantro, mint, and peanuts over the eggplant. Drizzle with the lime juice and some chili crisp, and serve with rice.