Using a vegetable peeler, peel half of the lemon zest into long ribbons. Julienne these ribbons into very thin slices for the fried lemon zest. Grate the other half of the lemon zest.
Add grated zest to a medium bowl with yogurt, lemon juice, fresh herbs, garlic, and oil. Mix and season to taste with kosher salt and black pepper. Let sit in refrigerator until ready to serve.
Add egg to a medium bowl. In a separate medium bowl, combine Panko, Italian breadcrumbs, sesame seeds, oregano, thyme, and black pepper. Dredge feta nuggets in egg wash, then dunk in breadcrumb mixture, making sure that the entire nugget is covered. Repeat with remaining nuggets. Transfer to a sheet pan or plate and freeze for 10 minutes.
Heat ¼ inch of oil in a large skillet over high heat. Fry julienned lemon zest until barely golden brown, about 30 seconds. Transfer to a paper towel lined plate. Once nuggets have chilled, fry them until golden brown on top and bottom, about 2 minutes per side. Transfer to a paper towel lined plate. Place on serving platter, top with fried lemon zest, then serve immediately with yogurt sauce, pita chips, and tomatoes.