In a food processor purée the strawberries and force the purée through a fine sieve into a saucepan. Add the honey and boil the mixture, stirring, for 3 minutes, or until it's thickened. Let the strawberry mixture cool to room temperature. Season with salt.
In a food processor or stand mixer, cream together the butter, the oil, and the strawberry puree until it's blended. Beat the mixture for several minutes, until the butter becomes smooth and creamy. Let the butter stand, covered, in a cool place for 1 hour to allow the flavors to develop. Store in an airtight container in the refrigerator.
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