Special equipment: a 10-inch cast-iron skillet
For the coulis: In a medium saucepan over medium-low heat, combine the raspberries, sugar, orange juice and vanilla. Cook, stirring frequently, until the raspberries are completely broken down and the sauce is syrupy, 10 minutes. Strain, a little at a time, through a fine-mesh sieve into a bowl, stirring to separate the seeds. Stir the orange zest in the strained sauce. Serve warm or set aside to cool. (The coulis can be stored in the refrigerator in an airtight container for up to 4 days.)
For the Dutch baby: Preheat the oven to 450 degrees F. Put a 10-inch cast-iron skillet in the oven to heat for 10 minutes.
Put the eggs in a large bowl and whisk vigorously until frothy. Whisk in the milk and then add the flour, vanilla and salt, and whisk until combined. Carefully remove the skillet from the oven and add the butter, swirling until it is melted and coats the pan. Pour in the batter and immediately return the skillet to the oven. Bake until the pancake is puffed and golden brown, 16 to 18 minutes.
Serve the Dutch baby with the raspberry coulis.