Rich Coffee Cake Dough, Food Processor Version

In bowl of food processor fitted with stainless steel blade, sprinkle yeast over warm water; add sugar, eggs, milk, and vanilla and pulse to mix, about four 1-second bursts. Add 1 1/2 cups flour and salt and process until smooth, about 20 seconds; scrape down sides of bowl. Distribute butter pieces over dough, sprinkle 1/2 cup flour over butter, and pulse until butter is incorporated, about twelve 1-second bursts. Scrape down sides of bowl and beneath blade if any dough has stuck there; remove half the dough from bowl and reserve. Process dough that remains in bowl until soft and satiny, about 1 minute. Remove processed dough and repeat processing with reserved portion. Combine both dough portions on lightly floured work surface, sprinkle with remaining 2 tablespoons flour, and form dough into ball.

Scrape dough (which will be too soft to pick up with hands) into straight-sided plastic container or bowl using plastic dough scraper. Cover container tightly with plastic wrap and let dough rise at warm room temperature until doubled in size, 3 to 4 hours. Punch dough down, replace plastic, and refrigerate until thoroughly chilled, at least 4 or up to 24 hours. Alternatively, for a quick chill, spread dough about 1-inch thick on baking sheet, cover with plastic, and refrigerate until thoroughly chilled, about 2 hours.