Pulse the raspberries in a food processor or blender until smooth.
Pour the puree through a metal sifter, pushing it through using a rubber spatula to remove the seeds. Discard the seeds. If it is too thick to push through a sifter, you can add a little water (you'll boil out the water in the next step.
Place the seedless puree into a saucepan over low-medium heat. Bring it to a gentle simmer while occasionally stirring. As the mixture boils it will thicken. The more it thickens, begin stirring constantly to avoid it burning or sticking to the bottom of the pan. When it's done, it should be a very dark red color and thick like jam. You should only have a few tablespoons of puree left.
Remove the puree from the heat and cool completely before using. It can be place in an airtight container in the fridge overnight.
Once the puree is completely cooled (it should not be warm to the touch), beat the butter in a large bowl until smooth.
Add in 2 cups of powdered sugar and beat into the butter, starting on a low speed and gradually increasing to medium speed.
Add in 2 tablespoons of the reduced raspberry puree and salt. Beat into the batter.
Beat in the rest of the powdered sugar about 1/2 cup at a time, alternating with a tablespoon of puree or cream until the desired sweetness and thickness is reached. More puree will make the frosting thinner (this is fine if frosting with a knife, but you may not want to do this if using a piping bag).
Frost the cooled cupcakes either with a knife or piping bag. I used a piping bag and 1M tip.