Step 1

Bring a large pot of lightly salted water to a simmer. Remove pot from heat and stir in noodles. Let soak, stirring often, until very al dente. Drain, reserving 1 cup noodle cooking liquid. Rinse noodles under cold running water.

Step 2

Mix gochujang and miso in a small bowl, gradually adding 1½ cups warm water, until smooth.

Step 3

Meanwhile, heat 3 Tbsp. oil in a large skillet, preferably nonstick, over medium-high. Add eggplant and drizzle with another 2 Tbsp. oil; season lightly with salt. Cook, undisturbed, until golden brown, about 3 minutes. Toss; continue to cook, tossing occasionally, until most of eggplant are golden and nearly tender, about 5 minutes more. Transfer eggplant to a plate.

Step 4

Reduce heat to medium and add remaining 1 Tbsp. oil to skillet. Cook garlic and ginger, stirring often, until golden, about 2 minutes. Add tomato paste and cook, stirring, until slightly darkened, about 1 minute. Stir in gochujang mixture and return eggplant to skillet. Cook, stirring occasionally, until eggplant are nearly falling apart, 6–8 minutes.

Step 5

Add noodles, butter, and ½ cup reserved noodle cooking liquid to skillet. Cook, tossing often and adding more cooking liquid as needed, until sauce is glossy, about 2 minutes; season with salt.

Step 6

Serve noodles topped with scallions and peanuts.