Spray a large baking pan with cooking spray. Put a broiler rack about 6 inches from the source of heat and preheat the broiler.

Combine the eggplant, fennel, 2 tablespoons of oil, garlic, and ½ teaspoon salt in a large bowl; toss to coat. Spread the eggplant-fennel mixture in a single layer in the pan. Broil until the vegetables are tender, stirring halfway through cooking (about 8 minutes). Transfer the pan to a wire rack and let the vegetables cool.

Meanwhile, in a medium nonstick skillet over medium-high heat cook the bacon, stirring occasionally, until crisp, about 6 minutes. Using tongs, transfer the bacon to paper towels to drain. Pour off all but 3 tablespoons of drippings in the skillet and return to medium heat. Add the shallot and cook, stirring occasionally, until tender, about 2 minutes. Remove the pan from the heat. Stir in the vinegar, the remaining ¼ cup oil, and the remaining ¼ teaspoon salt and bring to a boil. Remove from the heat and let cool slightly.

Combine the frisée, pine nuts, and mint in a large bowl. Drizzle with half of the warm dressing and toss to coat well. Arrange the frisée mixture on a platter. Top with the eggplant mixture. Sprinkle with the bacon and drizzle with the remaining dressing. Serve warm.