Over a large bowl with the paddle attachment, beat oil and sugar for 1 minute, at medium speed. Add eggs, one by one, beating after each addition. Add vanilla and sour cream and beat until just combined.
Include the hot coffee and the dry ingredients with the wet ingredients, alternating them. Start and finish with the dry ingredients and beat until just combined, scraping the bottom of the bowl. Do not overbeat.
Bake for 5 minutes. Reduce the oven temperature to 350 F and bake for an additional 7-10 minutes, or until a toothpick inserted in the middle comes out clean. Let the cupcakes cool for 1 minute in the cupcake tin, then place the unfrosted cupcakes over a wire rack to cool completely.
Sift your powdered sugar. Turn to low speed and gradually add your sifted icing sugar, vanilla extract, salt, and heavy cream until just combined. Turn the speed to high and beat for an additional minute. Scrape the sides of the bowl to ensure all of the ingredients are well-mixed. Frosting should look light and fluffy.