Whisk together flour, sugar, baking powder, and salt in a large bowl. In a separate bowl, beat the egg, then stir in milk, melted butter, and vanilla until smooth. Pour wet ingredients into dry ingredients and whisk until just combined. The batter should flow easily but not be too thin.

Pour oil into a large, heavy-bottomed pot until it reaches 2-3 inches deep. Heat to 375°F using a candy thermometer.

Transfer batter to a squeeze bottle or large zip-top bag with one corner snipped off.

Starting from the center, squeeze batter into hot oil in overlapping circles, creating a lacy pattern about 6 inches across. Fry for 2-3 minutes until golden brown on the bottom, then carefully flip with tongs and fry another 1-2 minutes.

Remove funnel cakes to paper towel-lined plates to drain excess oil. While still warm, generously dust with powdered sugar using a fine-mesh strainer.