In a bowl, whisk together the egg yolks, sugar, vanilla, and salt.
Pour the half-and-half and cream into the top of a double boiler** and heat over hot water until hot, but not boiling. Stir with a wooden spoon, scraping the bottom of the pan to prevent sticking.
**Note: I carefully heated the milk and cream in my microwave, being careful not to let it boil.
Slowly pour the hot cream into the eggs and whisk until smooth.
Return to the double boiler** and cook over medium-low until thick and bubbling around the edges.
**Note: I used direct heat, being very careful to stir constantly and to keep the temperature on medium-low. It took about 15 minutes for the custard to thicken, so be patient!
The custard will coat a wooden spoon.
Strain the custard through a fine-mesh sieve into a metal bowl. Cover and chill for at least 4 hours or overnight.
Rinse and hull the berries.
Sweeten the berries, with sugar, to taste.
I like to add about 2 tablespoons amaretto (or cognac), but this is optional.
Mash the the berries with a fork or potato masher; they will not be smooth but still a little chunky; divide in half.
Using a blender (or an immersion blender, which I prefe, puree the berries. If you wish, you can strain the puree to remove the seeds, but I leave them in.
Chill the berries for at least 1 hour, or overnight.
To make the ice cream, blend the chilled cream and pureed strawberries.
Turn on the machine, and then add the cream mix into the canister of an ice cream maker. Freeze according to manufacturer's instructions.
When the ice cream is the consistency of whipped cream, stir in the chopped berries.
Transfer to a shallow quart container, cover with plastic wrap, and freeze in the refrigerator's freezer for at least 3 hours until ready to serve.
Let the ice cream sit at room temperature for about 10 minutes before scooping.