Prepare the Cake: Preheat oven to 350°F. Grease (with butter) and flour a 10-inch, 12-cup light-colored metal tube (angel food) pan. Sift together flour, nutmeg, allspice, cinnamon, and salt into a large bowl.

Beat eggs in bowl of a stand mixer fitted with paddle attachment on medium speed until foamy, about 1 minute. Gradually add sugar, beating on medium speed until mixture is thick and pale, 2 to 3 minutes. Gradually add oil, beating until well combined. With mixer running on low speed, add flour mixture alternatively with buttermilk, beginning and ending with flour mixture, beating until just combined after each addition.  

Stir together water and baking soda in a small bowl until dissolved; add to batter with jam and vanilla. Beat on low speed until just combined. Gently fold in walnuts. Pour batter into prepared pan; spread into even layer. Bake in preheated oven until a wooden pick inserted into center of cake comes out clean, about 1 hour and 10 minutes. Cool on a wire rack 15 minutes. Invert and remove cake from pan to wire rack, and let cool completely, about 1 ½ hours.

Meanwhile, prepare the Glaze: Stir together sugar, cornstarch, buttermilk, butter, corn syrup, cornstarch, and baking soda in a medium saucepan over medium; bring to a boil, stirring occasionally. Cook, stirring occasionally, until sugar is dissolved and is light golden brown, about 5 minutes. Remove from heat; stir in vanilla, and let cool 30 minutes. Drizzle slightly warm glaze over cooled cake.