Blend eggs, milk, flour, melted butter, salt, and pepper until the mixture is completely smooth and lump-free.

Carefully remove the hot skillet, add butter, and swirl it to coat the bottom before quickly pouring in the batter.

Sprinkle parsley and scallions over the batter, then bake until the pancake is puffed and golden around the edges.

While the pancake bakes, heat butter and oil in a skillet, then sauté peas, garlic, and scallions until fragrant but not browned.

Add water and cook until the peas are tender and the liquid evaporates, then stir in parsley, salt, pepper, and lemon zest.

Remove the Dutch baby from the oven and top it with spoonfuls of Boursin cheese and the cooked peas.

Garnish with extra herbs if desired and serve immediately while warm.