Preheat oven to 375°F.
Combine 2 cups flour, undissolved yeast, sugar and salt in a large bowl. Add very warm water and oil; mix until well blended, about 1 minute. Gradually add enough remaining flour to make a soft dough. Dough should form a ball and will be slightly sticky. Knead** on a floured surface, adding additional flour if necessary, until smooth and elastic, about 4 minutes. Cover and let rest on floured surface while preparing fillings.
To make strombolis, divide dough into four portions. Roll 1 portion into a 10 x 8-inch rectangle on a floured surface. Spread desired fillings lengthwise down center of dough, leaving outer 1-inch free of filling. Fold short sides in 1 to 2 inches; fold remaining sides over. Pinch tightly to close. Carefully transfer to greased baking sheet. Repeat with remaining dough.
Bake for 18 to 22 minutes until lightly browned. Transfer to cooling rack to keep bottom crust crisp. Serve with pizza sauce or other sauce for dipping.
*If you don’t have a thermometer, water should feel very warm to the touch.
**To knead the dough, add just enough flour to the dough and your hands to keep the dough from sticking. Flatten dough and fold it toward you.Using the heels of your hands, push the dough away with a rolling motion. Rotate dough a quarter turn and repeat the “fold, push and turn” steps. Keep kneading dough until it is smooth and elastic. Use a little more flour if dough becomes too sticky, always working the flour into the ball of dough.