In a small bowl, dissolve the instant coffee powder in warmed milk. Add vegetable oil and vanilla extract; mix well.
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In a separate bowl, beat egg whites until foamy. Gradually add sugar in three parts, continuing to beat until stiff peaks form.
Add egg yolks one at a time to the meringue, mixing gently after each addition.
Sift all-purpose flour and cocoa powder together. Gently fold the dry ingredients into the egg mixture using a rubber spatula.
Pour in the coffee mixture and fold until the batter is well combined.
Grease the inner pot of the rice cooker with butter or oil. Pour the batter into the pot. Gently tap the pot to release any large air bubbles.
Set the rice cooker to the 'cook' setting. Cook for approximately 50 minutes or until a toothpick inserted into the center comes out clean.
Once cooked, allow the cake to cool slightly before removing it from the rice cooker. Let it cool completely before slicing and serving.
Dissolve Coffee: In a small bowl, dissolve the instant coffee powder in the hot water. Set aside to cool slightly.
Beat Butter: In a medium bowl, use an electric mixer to beat the softened butter until light and fluffy (about 2 minutes).
Add Sugar and Cocoa: Gradually add the powdered sugar and cocoa powder to the butter, beating on low speed until incorporated.
Add Coffee and Vanilla: Pour in the cooled coffee mixture and vanilla extract. Beat on medium speed until smooth.
Adjust Consistency: Add milk, one teaspoon at a time, until the icing is creamy and spreadable.
Frost the Cake: Once the cake is completely cool, spread the icing evenly over the top using an offset spatula or knife.