Place the strawberries in a blender or food processor. Process until completely smooth. (If desired, you can strain the mixture through a fine mesh sieve to remove the seeds.) Measure out ¼ cup of strawberry puree.
In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until soft and fluffy, about 3 minutes. Add the strawberry puree and beat until well combined. Scrape down the bowl.
With the mixer on low speed, add the powdered sugar in about a cup at a time. Stop and scrape down the bowl occasionally.
Once all of the sugar is added, beat in 2 tablespoons of cream and the vanilla. Beat on medium-low speed until fluffy, about 1 minute. Add the additional tablespoon of cream if needed for a smooth and fluffy frosting. Use the frosting immediately or cover and chill overnight. Bring to room temperature and beat again for 30 seconds to 1 minute or until fluffy and spreadable before using.
