Old-Fashioned Crumb Cake

Stir together yeast, 1/4 cup warm milk, and 1 tablespoon sugar in bowl of mixer until yeast is dissolved, then let stand until foamy, about 5 minutes. (If mixture doesn't foam, discard and start over with new yeast.)
Stir together lemon juice and remaining 3/4 cup milk and let stand until curdled, 1 to 2 minutes.
Add 3 3/4 cups flour to yeast mixture along with salt, eggs, vanilla, and remaining 1/2 cup sugar and mix at low speed until just combined. Add curdled milk and beat at medium speed until a dough forms. Add butter, 1 piece at a time, beating, then continue to beat until dough is silky and elastic, 5 to 8 minutes. (Dough will be very sticky.) Sprinkle with remaining 2 tablespoons flour and cover bowl with a clean kitchen towel (not terry cloth). Let dough rise in a draft-free place at warm room temperature until doubled in bulk, 1 1/2 to 2 hours.
Pulse together topping ingredients in a food processor until many large clumps form. Transfer to a bowl and chill, covered, until ready to use.
Butter a 13- by 9-inch baking dish or pan.
Stir dough several times with a rubber scraper to release air, then spread evenly in baking dish.
Sprinkle dough with half of topping, then cover dish with kitchen towel and let dough rise again in a draft-free place at warm room temperature until almost doubled in bulk, 1 to 1 1/2 hours.
Put oven rack in middle of oven and preheat oven to 350°F.
Sprinkle remaining topping over top of cake and bake until topping is golden, 55 to 60 minutes. Cool cake in pan on a rack until barely warm, then cut into squares.