Preheat your oven to 350 degrees and line a cupcake pan with 6 paper liners.
In a large bowl, whisk together the sugar, melted butter, and oil until combined. Whisk in the egg until just combined. In a small bowl, whisk together the flour, coffee granules, salt, baking powder, and baking soda. In another small bowl, stir together the milk and coffee. Add about 1/3 of the flour mixture into the sugar mixture and whisk until just combined. Then add about half of the milk mixture and whisk until just combined. Repeat until you've added all of the flour and milk to the large bowl. The mixture will look a bit streaky from the coffee granules, but that's ok!
Divide the batter evenly into your prepared 6 cupcake cups. They should be fairly full, and you should use all of the batter here.
In a small bowl, stir together the oil, flour, brown sugar, salt, and instant coffee granules using a fork until combined. The mixture should form small crumbs. Sprinkle the crumb topping on top of each cupcake and spread evenly. Bake the cupcakes for 15-18 minutes, or until a cake tester comes out clean. Cool completely before frosting!
In a large bowl, beat together the butter and sour cream until light and fluffy. Slowly add in the powdered sugar and beat for several minutes. The mixture should be very thick. Beat in the vanilla extract, instant espresso powder if you're using it, and salt. Then, slowly add in about 1 tsp at a time of the coffee, beating well between each addition, until the frosting has reached a fluffy, soft, pipe-able texture. You can't really over-beat the frosting, and it gets fluffier as you go! Frost cupcakes as desired, and enjoy!