Cut: Preheat oven to 400°F (204°C). Cut the eggplant in half, lengthwise. Score the eggplant, cutting 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 a cross hatch pattern. Brush with 1 Tbsp olive oil.
Bake: Place scored eggplant cut side down on a parchment lined baking sheet and bake for 20 minutes. Carefully flip eggplants to be cut side up, then return to the oven and cook for 10 more minutes.
Sauce: Meanwhile, combine all Sauce ingredients.
Serve: When eggplant has finished cooking, transfer to a serving plate. Top with mint sauce and crumbled feta cheese.