For the piquillo pepper sauce: Heat 1 tablespoon of the olive oil in a small skillet over medium-high heat. Add the onions and cook until soft, about 4 minutes. Add the garlic and cook for 30 seconds. Stir in the piquillo peppers, season with salt and pepper and cook for 5 minutes.
Transfer the mixture to a blender, and with the blender running, add the remaining 3 tablespoons olive oil and the vinegar and blend until smooth and silky. Add the creme fraiche and a touch of honey and pulse a few times just to incorporate; taste, pulse in a bit more honey if necessary. Transfer to a bowl.
For the empanadas: Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper and spray with nonstick spray.
Melt 2 tablespoons of the butter in a large nonstick skillet over high heat. Add the ham and cook, stirring occasionally, until golden brown, about 3 minutes; remove to a plate lined with paper towels.
Reduce the heat to low. Add the remaining 2 tablespoons butter and melt. Add the 8 whisked eggs and cook, stirring until soft curds barely form, then transfer to a bowl and quickly and gently stir in the green onion, goat cheese, ham and a generous amount of salt and pepper. Transfer to a baking sheet.
Roll each empanada wrapper on a lightly floured surface into a 7-inch round. Divide the filling among the wrappers, mounding it in the centers. Brush the edges with some of the egg wash. Fold each wrapper over the filling to create half-moon shapes and seal by pressing the edges together firmly with a fork.
Transfer the empanadas to the prepared baking sheet and brush with egg wash. Cut a few small slits in the top of each empanada to create steam vents. Bake until golden, about 10 minutes. Let cool for 10 minutes and serve with the piquillo pepper sauce.