Whisk the milk, egg, vanilla extract, and granulated sugar together in a large bowl until combined.
In a separate bowl, whisk the all purpose flour, salt, and baking soda until evenly mixed.
Pour the dry ingredients into the wet ingredients and stir until the batter is smooth and free of large lumps; do not overmix.
Add the unsalted butter (melted) once it has cooled to warm (not hot). Stir gently until just incorporated.
Pour oil for frying into a heavy skillet to a depth of about 1–2 inches and heat to 350–375°F (175–190°C), or until a small drop of batter sizzles and rises immediately.
Hold a funnel over the hot oil and fill it with batter. Use your finger to block the funnel tip while positioning it over the oil. When ready, release your finger and move the funnel in a circular/spiral motion to form a single spiral or desired shape.
Fry each funnel cake until puffed and golden brown on the first side (about 1–2 minutes), then flip carefully and cook the other side until golden brown.
Transfer the cooked funnel cake to paper towels to drain briefly, then repeat with the remaining batter, maintaining oil temperature.
Sprinkle the finished funnel cakes with powdered sugar and serve immediately.