In a large bowl, whisk together warm water, granulated sugar, and yeast; let sit until foamy.
Add eggs, softened butter, vanilla extract, and salt; mix to combine.
Gradually add flour, mixing until a soft dough forms.
Knead dough on a lightly floured surface until smooth and elastic.
Place dough in a greased bowl, cover, and allow to rise until doubled in size.
Roll the dough out to about ¼-inch thickness.
Cut dough into squares or rectangles.
Heat oil in a heavy pot or Dutch oven to 350°F (175°C).
Fry the dough pieces in batches until golden on both sides.
Remove and drain on paper towels.
Dust generously with powdered sugar before serving.