Prepare the Cake: Preheat oven to 325°F. Coat a 10-inch tube pan with cooking spray; dust with flour. Beat eggs, sugar, oil, and vanilla with a hand mixer on medium speed about 1 minute. Stir together baking soda, salt, cinnamon, and 2 1/2 cups of the flour in a separate bowl; gradually add to egg mixture, beating on low speed until blended.

Stir together apples, pecans, and remaining 1/2 cup flour in a bowl; fold mixture into batter. Spoon batter into prepared tube pan. Bake in preheated oven a until wooden pick inserted in center comes out clean, about 1 hour, 15 minutes. Cool in pan 15 minutes. Remove from pan; let cool until just warm, about 30 minutes.

Meanwhile, prepare the Frosting: Cook brown sugar, butter, and evaporated milk in a saucepan over medium, stirring often, until mixture comes to a boil and sugar is dissolved, about 2 minutes. Continue cooking, stirring constantly, until mixture reaches soft-ball stage (240˚F), about 3 minutes. Remove from heat; whisk until slightly thickened, abut 1 minute.

Drizzle Frosting over warm Cake. If desired, garnish with chopped pecans.