Position a rack in the center of the oven and place a 6-cup popover pan or a 12-cup muffin tin on it. Preheat the oven to 450°F and heat the pan for 10 minutes.
Melt the butter; reserve 1 tablespoon for greasing the cups and keep the remaining 2 tablespoons warm for the batter.
In a medium bowl, whisk the eggs until frothy, about 30 seconds. Whisk in the milk, vanilla extract, granulated sugar, and salt until combined.
Whisk in the flour until the batter is smooth and no dry bits remain, then whisk in 2 tablespoons of the melted butter. Let the batter rest for 10–15 minutes.
Carefully remove the hot pan and quickly brush the cups with the reserved 1 tablespoon melted butter. Divide the batter evenly among the cups, filling each about halfway.
Drop 3–4 fresh raspberries into each popover cup (2–3 if using a muffin tin), nudging them into the batter without stirring. Return the pan to the oven.
Bake for 20 minutes at 450°F without opening the oven door. Reduce the heat to 350°F and bake 15–20 minutes more, until tall, deeply golden, and the sides feel firm and crisp.
Remove the pan. Pierce each popover with a skewer to vent steam, then immediately unmold. Dust with powdered sugar and serve at once.