Here is my recipe for the buttercream I use as my go-to for all my cakes and it's perfect on red velvet and carrot cakes because it has cream cheese in it...it's a crusting frosting that holds up well to fondant decor...and it's delicious. I got the recipe from a bakery I worked for that used it all the time.
2 sticks (8 ounces) of real butter (I use salted Land 'o Lakes)
1 8 ounce package of cream cheese
2 pound package of powdered sugar.
Cream softened cream cheese and butter in mixer until well blended (about 5 minutes. The more you beat it, the whiter it gets, btw. Helpful if you need a whiter icing)
Slowly add powdered sugar until well blended. That's it!
No need for extra vanilla or other flavorings unless you want to. I use this as a base for my chocolate BC and all other flavors like lemon and coconut. It's very versatile. But it's perfect with red velvet and carrot cake as written.