In a medium saucepan, combine the half and half with salt and 1/4 cup sugar over low heat. Stir occaisionally for 5 minutes or until steam begins rise off the liquid. Remove from heat and set aside.
Beat the egg yolks and remaining 1/4 cup sugar together until color lightens a bit and gets thicker.
Stir 1/2 cup half and half mixture into the yolks, stirring well until combined. Add another 1/2 cup or so of the half and half and combine again. Then add the egg mixture back into the remaining half and half, stirring constantly until combined.
Return the liquid to low heat and stir constantly until thickened using the spoon test, about 4-5 minutes.
Set aside and allow the mixture to cool completely.
Strawberry puree
Core the strawberries and put 2/3 of them into a blender. Blend on high for a minute or two, until pureed.
Push the puree through a sieve to get the seeds out. You should have roughly 1 cup puree.
Dice the remaining strawberries and throw the in freezer.
Finish it off
When the half and half mixture is cool, stir in the cream and strawberry puree.
Pour half the liquid into the ice cream maker canister and then add half the strawberries from the freezer. Add the rest of the liquid and top with strawberries.
Churn according to your ice cream maker's instructions. I find it's usually about 25 minutes, and the sound changes pitch when the ice cream is ready.