Core the strawberries to remove the centers.
Place the berries in a food processor or blender and pulse until it's a smooth puree.
To remove the seeds, pour the puree through a metal sifter and push it through using the back of a spoon or rubber spatula. You will likely need to do this in a few additions. Discard the seeds.
Transfer the puree (without seeds) to a saucepan over low-medium heat. Gently boil as you occassionally stir the puree. As it boils, it will begin to thicken and darken in color.
Once the puree is thick like jam and very dark (about 15 minutes), remove from the heat and cool fully. You should have about ¼ cup or less. You can speed this up by transferring to a jar or bowl and placing in the fridge or freezer.
In a large bowl, beat together the butter until fluffy.
Add in 2 cups powdered sugar and beat together, starting with the mixer on a low speed.
Turn off the mixer and add in 2-3 tablespoons of the reduced and cooled strawberry puree. Beat until combined.
Mix in the rest of the powdered sugar about ½ cup at a time, adding in 1-2 more tablespoons of reduced and cooled puree as necessary until the desired sweetness and thickness is reached. If the frosting is starting to separate or look too thin, do not add in any more puree. Beat in 1 tablespoon whipping cream, if the frosting seems to thick.
Frost the cooled cupcakes using a knife or transfer the frosting to a piping bag (I used a 1M tip) and frost.