Cut the eggplant in half, lengthwise. Score the eggplant so that you cut slits into just the flesh (not the skin), making about 5 cuts diagonally across the eggplant. Make another set of cuts diagonally the other way to create sections that look like diamonds (see picture). Brush with 1 Tbsp olive oil and set on a baking tray. Bake at 400 degrees F for 35 to 40 minutes, or until tender.
Meanwhile, combine 2 Tbsp olive oil, lemon juice, mint, garlic, salt, and pepper in a food processor until smooth,
When eggplant has finished cooking, transfer to a serving plate. Top with mint sauce and crumbled feta cheese.