In a medium saucepan, combine water, butter, 2 tablespoons sugar, and salt. Bring to a rolling boil over medium-high heat, stirring occasionally until butter melts completely.

Remove from heat and immediately add the flour all at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan, about 1 minute.

Let the dough cool for 5 minutes, then beat in eggs one at a time, mixing until fully incorporated and smooth after each addition. Stir in vanilla extract, then gently fold in diced peaches until evenly distributed.

Transfer dough to a piping bag fitted with a large star tip. In a shallow bowl, whisk together 1 cup sugar and cinnamon for the coating and set aside.

Heat 2-3 inches of vegetable oil in a heavy-bottomed pot or deep skillet to 350°F. Test with a small piece of dough—it should sizzle immediately and rise to the surface.

Pipe 4-5 inch strips of dough directly into the hot oil, using scissors to snip the ends. Fry 3-4 churros at a time without crowding, turning once, until deep golden brown on all sides, about 3-4 minutes total.

Remove churros with a slotted spoon and drain briefly on paper towels for 10 seconds, then immediately roll in cinnamon sugar while still hot and glistening.

Let coated churros rest on a wire rack for 2 minutes to set the coating before serving warm.