Heat oven to 350°F. Lightly whisk eggs, half-and-half, 1 teaspoon tarragon, the nutmeg, salt and pepper in a medium bowl and set aside.
Melt butter in a Field No.4 Skillet. Add bread and toast, flipping once, until golden on both sides, 5–6 minutes. Transfer to the bowl with egg mixture, turn to coat, and set aside.
Return skillet to medium-high. Add asparagus and cook until slightly softened and bright green, about 2 minutes. Stir in scallions and season with salt and pepper. Remove the asparagus and scallions from the pan and remove the pan from the heat.
Return the bread to the skillet and scatter the asparagus and scallions over top. Pour the egg mixture into the skillet, top with the crumbled feta and remaining ½ teaspoon tarragon. Bake until puffed and golden and just set at the center, 15–18 minutes.
