Preheat oven to 450 degrees. Toss ramps with 1 tablespoon olive oil and spread on a baking sheet. Roast until softened and charred in spots, 5-8 minutes. Let cool; chop.
Coat the same baking sheet with 1 tablespoon oil. Stretch the dough on it to form a 16 x 6" oval. Place in the oven and bake until golden brown and puffed, 8–10 minutes.
While crust is baking, fry two eggs in a skillet.Remove flatbread from oven and spread with Nduja, leaving a crust. Top pizza with mozzarella pieces and place back in the oven until cheese it slightly melted. Remove and top with 2 fried eggs. Scatter with greens and ramps. Cut into slices and serve.