This coffee cake recipe comes from Cook's Illustrated. It is suggested that this is best eaten the day it is prepared. It has a very dense batter, so be sure to use your electric mixer, rather than trying to mix by hand.
Heat 1 tablespoon butter in a 10-inch skillet (preferably nonstick) over high heat until golden. Add apples, cover, and cook over high heat, stirring frequently, until they are dry and very tender, 2 to 3 minutes.
Remove from heat, sprinkle apples with 2 tablespoons sugar, and lightly toss until glazed.
Cool to room temperature.
Adjust oven rack to center position and heat oven to 350 degrees.
Generously grease bottom and lightly grease sides of 10-inch springform pan.
Sprinkle bottom of pan with dry bread crumbs, then shake lightly to coat.
Tap out excess crumbs.
Whisk flour, remaining sugar, and salt in large mixing bowl until blended.
Add remaining 10 tablespoons of butter and cut with whisk until mixture resembles coarse crumbs.
Remove 1 cup of crumbs to separate bowl.
Whisk 1 teaspoon cinnamon, baking powder, and baking soda into mixture remaining in large mixing bowl.
Add buttermilk or yogurt, egg, and vanilla; whisk vigorously until batter is thick, smooth, fluffy, and frostinglike, 1 1/2 to 2 minutes.
Fold in apples using a rubber spatula, then scrape batter into prepared pan and smooth top.
Add nuts, brown sugar, and remaining teaspoon cinnamon to reserved crumbs; toss with a fork or your hands until blended.
Sprinkle crumbs over batter, pressing lightly so that mixture adheres.
Bake cake until center is firm and cake tester comes out clean, 50 to 55 minutes (See Tip *).
Transfer cake to rack; remove pan sides.
Let cake cool completely, about 2 hours, before serving.
When completely cooled, cake can be slid off pan bottom onto serving plate.
*Do not insert a skewer into this cake to test for doneness until the center appears firm when the pan is shaken. If you do, the topping may squeeze air out, and the middle of the cake may sink.