Position rack in middle of oven and preheat to 425°F.
Scatter peanuts in a pie plate and toss them with 1 teaspoon oil and a generous pinch of salt. Roast, shaking pan once or twice, until peanuts are a golden brown (about 5 minutes). Set aside to cool and then coarsely chop them up.
Reduce oven temperature to 375℉.
Rinse the eggplant. Trim off tops and then cut eggplant in half lengthwise. In a large shallow pan, toss eggplant with 2 tablespoons of the oil and the red pepper flakes. Put eggplant cut-side-up on a rimmed baking sheet and sprinkle generously with salt. Roast until eggplant is tender when pierced with a fork and the flesh has turned a light golden brown, 10 to 12 minutes.
While eggplant is roasting, whisk 3 tablespoons oil with lime juice, honey and ¼ teaspoon salt in a small bowl. Season to taste with more salt, if necessary.
With the eggplant still on the center rack, turn the broiler on high and broil the eggplant until well-browned on top, about 5 minutes.
Transfer eggplant to a serving platter. Drizzle with dressing and sprinkle with mint and peanuts. Serve immediately.