Over a small bowl, press strawberry pieces through a fine sieve, pressing with the back of a spoon to yield about 1/4 cup or more of juice; use remainder of berries in sieve in a smoothie!
Place strawberry juice, grapefruit zest and juice, basil leaves, sugar, and eggs in metal bowl, whisk all ingredients to combine well, then add butter pieces.
Over simmering water in medium saucepan, place bowl (double-boiler fashion).
Whisking constantly, cook until thickened and smooth, and instant-read thermometer registers 160F, about 5-7 minutes. Do not overcook as eggs will begin to coddle!
Remove bowl from heat immediately, and strain with fine sieve set into another (preferably glass) bowl.
Serve warm or place waxed paper directly over curd and allow to cool/chill completely. May keep refrigerated for up to one week.