In the bowl of a large stand mixer, fitted with a paddle attachment, dissolve yeast in warm water. Let stand 5 minutes until foamy, then whisk in sugar, oil, yogurt, and salt until smooth. Add 4 cups flour to mixer, and mix on medium speed, adding additional flour by the tablespoon until dough is smooth and pulls away from sides of bowl.
Turn dough onto a floured surface and knead several minutes until dough is smooth and elastic. Place dough in a greased bowl, turning once to grease top. Cover bowl with plastic wrap and let rise in a warm place until dough is doubled in size, about 1 hour.
Punch risen dough down and divide into 18 portions. Roll each portion into a 12-in rope and twist several times. Place twists on parchment paper-lined baking sheets, cover with plastic wrap and let rise 30 minutes until doubled in size.
Remove plastic wrap and bake twists at 375F 20-25 minutes or until golden brown. Remove from oven and brush twists with melted butter. Enjoy twists warm from the oven!