In a large bowl with a whisk by hand, mix together the flour, salt, and sugar. Add eggs and vegetable oil, and water, and mix until dough is smooth. Cover with plastic wrap and allow to rest for 30 minutes at room temperature.
Adjust oven rack to lower-middle position and preheat oven to 425 degrees. Line a large rimmed baking sheet with parchment paper (add melted butter to the parchment if desired; see note 1).
On the counter, lay a clean kitchen towel down and lightly dust with flour. Divide dough into two pieces. Place one piece of the dough onto the floured towel and using a rolling pin, roll out into a rectangle shape, about 1/8 inch thick.
Place half of your preferred filling mixture along the long edge of the dough. using the kitchen towel to assist, roll the dough around the filling tightly. Repeat with the remaining dough and filling.
Place both strudels seam-side down onto the prepared baking sheet (brush with an egg wash if desired; see note 2). Place in oven and bake until crust is golden brown, about 25-30 minutes. Allow to cool completely on the baking sheet.
Butter: Like phyllo dough, some strudel doughs are brushed with butter before baking for a richer taste. We often add 1 cup (2 sticks) melted butter straight to the baking sheet, on top of the parchment, for a similar result.
Egg wash: For a rich golden brown color, beat 1 egg with 1 tablespoon water and brush on the formed strudels before baking.
Yield: This recipe makes enough strudel dough for 2 long strudels, enough for about 8 dessert or brunch side dish-size servings.
Make ahead: Store the strudel dough (before rolling, wrapped in plastic wrap) for up to 2 days in the refrigerator. Let it sit out at room temperature for 30 minutes before rolling.
Freezer: Wrap, date, and label the strudel dough and freeze for up to 3 months. Thaw overnight in the refrigerator or at room temperature, then roll out, fill, and bake as directed in your recipe.
Tools of the trade: Use a woven towel (not a terrycloth towel) towel to roll the strudel so it doesn’t stick to the dough.