In a medium saucepan melt butter over medium heat. Reduce heat to medium-low. Continue to cook, without stirring, for 5 to 6 minutes or until butter becomes brown and fragrant. Remove from heat; cool slightly. Transfer to a small bowl. Cover and chill for 2 hours or freeze for 30 minutes or until firm.
Preheat oven to 325°F. Grease and flour a 10-inch fluted tube pan or coat with nonstick spray for baking; set aside. For filling, in a small bowl combine 3/4 cup of the pecans, 1/2 cup of the brown sugar, and the 2 teaspoons flour. Add 3 tablespoons of the browned butter and work in with fingers or a fork until mixture is crumbly; set aside. In a medium bowl stir together the 3 cups flour, the baking powder, baking soda, and salt; set aside.
In a large bowl beat remaining browned butter with an electric mixer on medium to high speed for 30 seconds. Add remaining 1-1/2 cups brown sugar; beat until combined, scraping side of bowl occasionally. Add eggs, one at a time, beating after each addition until combined. Stir in vanilla. Alternately add flour mixture and yogurt to butter mixture, beating on low speed after each addition just until combined. Stir in remaining 1-1/4 cups pecans.
Spoon half of the batter into prepared pan, spreading evenly. Sprinkle batter in pan evenly with filling. Spoon remaining batter over filling, spreading to cover.
Bake about 50 minutes or until a toothpick inserted near the center comes out clean. Cool in pan on a wire rack for 10 minutes. Remove from pan. Cool about 45 minutes before serving. Drizzle with Coffee Icing before serving.
In a small bowl stir together milk and instant coffee crystals until coffee is dissolved. Stir in powdered sugar and enough additional milk to make icing a drizzling consistency.