Preheat the oven to 425°F to ensure it’s fully heated before you bake.
In a large mixing bowl, combine the flour, salt, and black pepper, whisking until evenly mixed. In a separate bowl, beat together the eggs and milk until smooth. Gradually pour the wet ingredients into the flour mixture, whisking gently until just incorporated. Stir in the chopped thyme and chives.
Place a 12-inch cast-iron or oven-safe skillet on medium-high heat and add the butter. Let the butter melt completely and cook for 5 to 7 minutes until it turns golden brown and develops a nutty aroma. Carefully tilt the skillet to coat the entire bottom with butter.
Pour the prepared batter into the hot skillet. Evenly sprinkle the Parmesan cheese over the top, followed by a light sprinkling of flaky sea salt. Transfer the skillet to the oven and bake for 20 to 25 minutes, or until the Dutch baby puffs up and turns golden. For a softer, more custardy center, opt for a shorter baking time, while a longer bake will result in a crisper texture.
Remove from the oven and serve immediately. Garnish with additional thyme and chives for a fresh, aromatic touch. If desired, add a side of Sriracha or lemon wedges to enhance the flavors.