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Preheat the oven to 350°F. If using a convection oven, reduce the temperature to 325°F. Grease and line two 8-inch round cake pans with parchment paper.
In a large bowl, beat 1 cup unsalted butter and 1 cup granulated sugar with an electric mixer on medium speed until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition. If the batter starts to look curdled, beat in 1 tablespoon self-rising flour.
In a small bowl, dissolve 2 tablespoons instant coffee granules in 2 tablespoons hot water; let cool slightly. Stir the coffee mixture into the batter until combined.
Gently fold in 1 3/4 cups self-rising flour until just combined, then fold in 1 cup chopped walnuts.
Divide the batter evenly between the prepared pans, smoothing the tops with a spatula. Bake for 20 to 25 minutes, or until golden and a toothpick inserted into the center comes out clean.
Let the cakes cool in the pans for 10 minutes, then transfer them to a wire rack to cool completely.
For the coffee buttercream, in a small bowl, dissolve 1 tablespoon instant coffee granules in 1 tablespoon hot water; let cool.
In a medium bowl, beat 3/4 cup unsalted butter until creamy. Gradually add 2 1/2 cups powdered sugar, beating well after each addition. Add the coffee mixture and 1 1/2 tablespoons whole milk, then beat on high speed until light, fluffy, and spreadable.
Place one cake layer on a serving plate. Spread half of the frosting over the top. Top with the second layer, spread with the remaining frosting, and garnish with walnut halves.