How to Make It
Pour vegetable oil to a depth of 2 1/2 inches in a large, deep Dutch oven; heat over medium-high to 350°F.
Whisk together flour, cornstarch, and 3 teaspoons chile-lime seasoning in a large shallow bowl, and set aside.
Cut1 lemon into thin slices; remove and discard seeds. Cut remaining lemon in half; squeeze 1 lemon half to equal 1 tablespoon juice, and set aside. Reserve remaining lemon half for another use.
Working in batches, dredge halloumi, lemon slices, pepperoncini, and olives in flour mixture, shaking off excess, and add to hot oil. Fry until golden brown and crisp, 3 to 4 minutes, turning halfway through frying. Using a spider or slotted spoon, remove fritto misto from oil, and drain on a wire rack set inside a baking sheet. (Adjust heat between batches to maintain temperature as needed.)
Whisk together yogurt, mayonnaise, mustard, reserved lemon juice, and remaining 1 teaspoon chile-lime seasoning in a small bowl until blended. Transfer fritto misto to a serving platter; garnish with mint, and serve with chile-lime sauce.