Stir together pecans, cinnamon, 1 cup of the flour, 1 cup of the brown sugar, and 1 teaspoon of the salt in a bowl. Add chilled butter pieces. Pinch and smear mixture between your fingers until butter is evenly incorporated and mixture starts to clump together. Cover and chill until ready to use (up to 24 hours).

Preheat oven to 350°F. Beat softened butter, granulated sugar, and remaining 1/2 cup brown sugar with a stand mixer fitted with a paddle attachment on medium-high speed until light and fluffy, 4 to 5 minutes. Add eggs, 1 at a time, beating well after each addition. Stir in vanilla.

Stir together baking powder, baking soda, and remaining 2 1/2 cups flour and 1/2 teaspoon salt in a bowl. Add baking powder mixture to softened butter mixture alternately with sour cream in 3 additions, beginning and ending with baking powder mixture, beating on low speed until just combined after each addition.

Lightly grease a 10-inch tube pan with shortening; dust with flour. Spoon half of the sour cream batter into prepared pan; top with half of the pecan mixture. Repeat layers once using remaining sour cream batter and pecan mixture. Bake in preheated oven until a wooden pick inserted in center comes out clean, 45 to 55 minutes, tenting with foil after 35 minutes if needed to prevent excessive browning. Cool cake in pan on a wire rack 15 minutes; invert cake onto wire rack, and let cool completely, about 2 hours.