1 1/2 cups butter, at room temperature (I like to use 3/4 cup salted and 3/4 cup unsalted)
3 3/4 cups powdered sugar
3/4 cup cocoa powder*
3 - 4 Tbsp heavy cream or half-&-half
1 1/2 tsp vanilla extract
In a the bowl of an electric stand mixer, fitted with whisk attachment (paddle attachment works too. Whichever you use just pay attention the the shade of the butter), whip butter on moderately high speed until very pale and fluffy (nearly white in color), about 6 - 8 minutes, occasionally scraping down sides of the bowl. Sift in cocoa powder then add in powdered sugar, 3 Tbsp heavy cream and vanilla and mix on low speed until combine, scrapping down the sides of the bowl as needed and adding up to 1 tbsp additional cream to thin if desired. Increase mixer to medium-high speed and whip mixture until pale and very fluffy about 4 - 5 minutes, occasionally scraping down sides of the bowl.
Note that similar to whipped cream the frosting will lose some of its "fluff" after a few hours, it will still taste the same it just loses some of the air that was whipped into it (similar to whipped cream how it loses it's stabilization after a few hours). It is best to prepare and use within a few hours for best (fluffiest) results.