Prep canister. Prepare ice cream maker by freezing the canister. Many machines require at least 24 hours of chilling, so don’t forget to do this first.
Make the strawberry syrup. Combine the sliced strawberries, lemon juice, and ¼ cup of sugar in a small saucepan. Bring to a simmer over medium-low heat and simmer for 3 minutes. Turn off the heat and mash with a potato masher or fork until it is like a sauce with some berry pieces still intact. If you do not want pieces of berries in the finished ice cream, run it through a food processor or use a stick blender.
Heat the milk. Add the milk, cream, and ½ cup of sugar to a large saucepan. Over medium heat, warm the mixture until it is very warm (175℉), for about 5 minutes. It should be steaming but not simmering
Beat the eggs. While the mixture is heating, combine the egg yolks with the remaining cup of sugar. Beat until it turns lighter yellow in color. A hand mixer works well for this.
Temper the eggs. Remove the milk mixture from the heat, and add half a cup at a time to the egg mixture. Mix after each addition. Add until half the milk mixture is gone. Adding the warm milk slowly prevents it from cooking the eggs. Once you’ve added about half of the milk mixture into the eggs, pour the entire milk-egg mixture back into the saucepan. Heat over medium and cook, stirring constantly, until the mixture is 185℉, or has thickened enough to coat the back of a spoon. Do not boil.
Strain and chill. Remove the custard from the heat and stir in the salt. Strain the mixture using a strainer or cheesecloth set over a large bowl. Allow it to cool at room temperature, then cover and place it in the fridge until very cold- at least 6 hours, up to overnight. Cover and refrigerate the strawberry syrup too.
Churn. Remove custard from fridge and set up ice cream maker, according to manufacturer's instructions. Pour custard in and churn until it is the consistency of soft serve ice cream, then add the strawberry mixture. Let the machine run a few more minutes until the ice cream is pink and the berries are distributed throughout.
Freeze. Place in a freezer-safe loaf pan, cover, and refreeze for 2-4 hours until hardened. Scoop and serve. It will last up to one week in the freezer, stored in an airtight container with plastic wrap pressed on top. Let the ice cream sit at room temperature for a few minutes before scooping.