Preheat oven to 400 degrees. Butter a shallow 2-quart baking dish with butter; set aside.

Fill a medium saucepan with water and bring to a boil; add salt and return to a boil. Prepare an ice-water bath and set aside. Add asparagus and cook until crisp-tender, 1 to 2 minutes. Drain and transfer to ice-water bath to cool. Drain, pat dry, and set aside.

Place potatoes in a medium saucepan and add just enough cold water to cover. Add 2 tablespoons salt and bring to a boil over high heat. Reduce heat to a simmer and cook until potatoes are just cooked through, about 8 minutes; drain and set aside.

In a large bowl, whisk eggs, cream, 1 teaspoon salt, and 1/2 teaspoon pepper to combine. Add potatoes, parsley, chopped herbs, goat cheese, and scallions; stir to combine. Transfer egg mixture to prepared baking dish; sprinkle with Gruyere and scatter asparagus over top. Press down on asparagus to submerge.

Transfer to oven and bake for 30 minutes, rotating halfway through baking. Reduce oven temperature to 350 degrees and bake until golden, puffed, and just set in the center, about 10 minutes more. If top begins to brown too much before eggs are set, cover with parchment paper-lined aluminum foil. Serve warm or at room temperature with herbed creme fraiche.