Mix milk, flour, eggs, butter, sugar, and salt together in a bowl. Transfer batter to an electric blender and combine on high speed until blended; it's fine if batter has some lumps. Let rest for 15 minutes.

Meanwhile, heat vegetable oil in a pan over medium heat. Add ham and cook until heated through, 3 to 4 minutes. Add onion and cook until softened, about 5 minutes more. Reduce heat to low and stir in spinach and tomato. Keep warm.

Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.

Heat a nonstick skillet over medium heat and lightly coat with cooking spray. Pour 1/3 cup batter into the skillet, swirling to cover the pan. Cook until underside of crepe is lightly brown, 1 to 3 minutes. Loosen edge of crepe and flip. Cook until lightly browned, 1 to 2 minutes more. Set aside; repeat with remaining batter.

Place crepes onto the prepared baking sheet. Add ham-veggie mixture to the center of each crepe. Crack an egg carefully over ham mixtures. Fold edges of crepes inward.

Bake crepes in the preheated oven until egg whites set, 8 to 11 minutes. Top crepes with parsley and season with salt and pepper.