For the pan-fried mint:
Heat a small frying pan over medium-high heat. Add 2 tablespoons of the oil and the mint leaves. Sauté until the leaves are crisp and dark green, stirring continuously, about 1-2 minutes. Transfer to a small bowl and add the remaining olive oil. Set aside.
For the dip:
Place the beans, garlic, lemon juice, oil, salt, and pepper, to taste, in the bowl of a food processor. Process, scraping the sides of the bowl once, until smooth, about 1 minute. Transfer to a serving bowl. Make a well in the center of the dip, pour the fried mint and its oil inside, and serve.