Toss arugula with lime juice in a small bowl; season with salt and pepper.
Heat olive oil in a medium skillet over medium-high. When the oil is hot, crack both eggs into skillet and season with a pinch of Desert Deep Dish. Oil should be bubbling around eggs from the start. Cook, rotating skillet occasionally until whites are golden brown and crisp at the edges and set around the yolk (which should be runny), about 2 minutes.
Meanwhile, toast the bread until browned and crisp. Lightly rub 1 side of each slice with the cut side of the garlic until fragrant; discard the garlic.
Mash the avocado with a fork in a shallow bowl until chunky and stir in the feta cheese and the rest of the Desert Deep Dish. Spread the mashed avocado evenly among the toasts, and top with the fried eggs. Spoon any remaining Olive Oil from the skillet on the eggs, and top with arugula.
