Preheat the oven to 375°F. Lightly grease a rimmed baking sheet using about 1 teaspoon of olive oil to prevent sticking and ensure even cooking.
Prepare the asparagus by slicing the bottom ends on a sharp bias into ¼-inch thick pieces. Reserve the top 4 inches of each spear, halving them lengthwise—or quartering if they're particularly thick—for a more delicate texture and presentation.
In a large mixing bowl, whisk together the eggs, milk, Dijon mustard, 1 teaspoon of kosher salt, and ½ teaspoon of freshly ground black pepper until the mixture is smooth and frothy. Fold in the sliced spinach and the bias-cut asparagus ends, mixing to distribute evenly.
Pour the egg mixture into the greased baking sheet, spreading it out in an even layer. Arrange the reserved asparagus tops over the surface, gently pressing them in. Sprinkle the crumbled goat cheese over the top for bursts of tangy creaminess throughout the frittata.
Bake on the center rack, rotating the pan halfway through the cooking time, for 20 to 22 minutes or until the eggs are set, puffed, and no longer jiggly in the center. Allow the frittata to rest for 5 minutes before slicing into squares and serving warm or at room temperature.