Pat the halloumi block dry with paper towels and cut it into 1/2-inch thick fries.
Set up a breading station with three shallow bowls: one for flour, one for the beaten egg, and one for the panko breadcrumbs.
Coat each halloumi stick evenly in flour, dip it into the beaten egg, and firmly press it into the panko breadcrumbs until completely covered.
Heat the vegetable oil in a large skillet over medium-high heat. Fry the breaded halloumi sticks for 2 to 3 minutes per side until they are golden brown and crispy.
Transfer the fried cheese sticks to a paper towel-lined plate to drain any excess oil.
In a small bowl, whisk together the Greek yogurt, lemon juice, lemon zest, and chopped mint to create the white dipping sauce.
Serve the warm crispy halloumi fries immediately alongside the fresh mint dipping sauce.