Place all but 5 of the strawberries into a food processor and pulse the strawberries until you get almost a 'slushy' type of texture, set aside. Chop the remaining 5 strawberries into tiny pieces, set aside. Place a fine mesh strainer over a large bowl, set aside.
In the bowl of an electric mixer fitted with the whisk attachment, beat the egg yolks and the remaining 1 cup of sugar together for 2 minutes, set aside.
In a medium saucepan over medium heat, heat the milk and cream together until just below boiling point (you'll notice bubbles form around the edges of the pot on the surface of the milk). DO NOT LET MILK BOIL.
With the mixer on the low setting (just above stir), add 1/4 cup of the hot milk into the egg yolks. Add another 1/4 cup in while the mixer is running. Turn the mixer off. Add the yolks into the saucepan with the remaining milk/cream. Cook on medium low until it thickens, about 7-9 minutes stirring continuously.
Strain the ice cream mixture through the mesh strainer. At this point, you can strain the strawberry puree if you would like to remove the seeds. If not, remove the mesh strainer, add the strawberry puree, chopped strawberries, vanilla extract, and salt into the mixture. Cover the surface of the ice cream custard with plastic wrap and allow to cool in the refrigerator for at least 5-6 hours or preferably overnight.
Freeze in your ice cream maker, according to directions. Keep in mind, if you have a small ice cream maker, you may need to freeze in two batches. Serve soft serve ice cream fresh from the ice cream maker or let cool in the freeze. Ice cream can be kept frozen for up to 1 month (if it lasts that long!) Remove ice cream from freezer 5 minutes before serving, this will make scooping out the ice cream much easier.