Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
In a medium mixing bowl, combine the shredded carrots, shredded mozzarella, and the egg until a uniform batter forms.
Transfer the carrot mixture to the prepared baking sheet and spread it into a thin, even 8-inch circle.
Bake the carrot tortilla for 15 to 18 minutes until the edges are golden brown and the center is firm to the touch.
While the tortilla bakes, season the chicken breast on both sides with garlic powder, sea salt, and black pepper.
Heat the olive oil in a grill pan or skillet over medium-high heat and cook the chicken for 5-7 minutes per side until fully cooked.
Remove the chicken from the heat and let it rest for 3 minutes before slicing into thin strips.
Carefully peel the carrot tortilla off the parchment paper and place it on a plate.
Spread the Greek yogurt over the surface of the tortilla, then layer with fresh baby spinach and the grilled chicken strips.
Roll the tortilla tightly and serve immediately while the wrap is still warm.