Heat the oven. In a large bowl, whisk together the flour, Kosher salt, and black pepper. In a separate bowl, whisk together the eggs and milk or heavy cream. Whisk the eggs into the flour mixture until just combined, then stir in fresh thyme and chives or tarragon.
Melt unsalted butter in a cast-iron or other oven-safe skillet over medium-high heat. Continue to cook until the butter turns brown, then swirl the skillet so the butter coats the bottom of the pan.
Pour the batter into the skillet, and scatter Parmesan cheese and a generous pinch or two of flaky sea salt over the top. Bake until the Dutch baby is puffed and golden. Baking it a little less gives a softer interior though less rise.
Serve immediately, garnished with thyme and chives!