1. To make dough, sprinkle yeast over warm water in a large bowl. Let stand until foamy, about 5 minutes.
2. Combine yogurt, sugar, melted butter, egg, and salt in a small bowl; add to yeast mixture. Add 2 cups of flour, 1 cup at a time, beating after the first addition with a whisk and after the second addition with a wooden spoon. Mix in remaining flour with your hands. (You might need to add tiny amounts of additional flour or nonstick spray to both your hands and the dough to prevent sticking. Keep the flour to a minimum so the dough can remain soft.)
3. Knead the dough in the bowl until all the flour is incorporated and you have a smooth, slightly sticky dough. Lift the dough and spray the bowl with nonstick spray. Set the dough back in the bowl and spray the top with nonstick spray. Cover with a clean kitchen towel and let rise in a warm place until dough has increased in bulk by 50 to 75 percent, at least 1 hour.
4. In a small bowl, combine sugar and cocoa. After dough has risen, punch it down. Lightly spray a clean work surface with nonstick spray. Turn dough out onto prepared surface and let rest, 5 minutes. Gently stretch and press the dough into a 10x16-inch rectangle (use a little flour if it's too sticky). Spread dough with melted butter, leaving a half-inch border around the edges. Sprinkle the sugar mixture over the butter, then scatter with chocolate chips. Roll up the dough lengthwise, gently stretching it over the filling. Pinch the seam closed. Transfer babka to a greased cookie sheet, seam side down. Curve the babka if necessary to fit and let rise in a warm place, about 1 hour more.
5. Adjust rack to middle of oven. Heat oven to 350 degree F. Bake until babka is lightly browned and feels hollow when gently squeezed, 30 to 40 minutes. Brush the top with beaten egg halfway through. Cool on a wire rack at least 30 minutes before serving. Makes 16 servings.