Whisk the flour, powdered sugar, baking powder and salt in a large bowl. Whisk the milk, egg, oil and vanilla in a small bowl until smooth. Form a well in the dry ingredients and pour in the wet ingredients. Stir slowly just until all the dry ingredients are moistened; the batter may be a little lumpy. Let stand while the oil heats.
Fill a large, high-sided skillet or large pot with oil to a depth of 2 inches. Heat over medium-high heat until a deep-fry thermometer registers 365 degrees; if you add a drop of batter to the oil, it should immediately rise and start sizzling steadily but not violently.
Transfer the batter to a large resealable plastic bag. Snip a ¼-inch hole in one corner. Holding the bag about 2 inches above the oil, swirl one-quarter of the batter (about ½ cup) out of the hole in concentric circles and squiggles to form a 6- to 8-inch-diameter cake.
Fry, adjusting the heat as needed to maintain the temperature, until golden brown on the bottom, about 2 minutes. Using tongs, chopsticks or two forks, carefully flip the cake and fry until the other side is golden brown, 1 to 2 minutes longer. Carefully transfer to paper towels to drain, then dust with powdered sugar to coat while hot. Repeat with the remaining batter, replenishing and reheating the oil between batches as needed.
Mound as much whipped cream as you want on the sugared funnel cake, then crush a handful of marshmallows over the whipped cream like sprinkles. Scatter whole marshmallows on top and serve immediately.
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