In a medium bowl lightly whisk the yolks together with a 1/4 cup of the sugar. Set aside.
In a non-reactive saucepan combine the remaining 1/4 cup of sugar, 1 1/2 cups of the cream, and the salt. Heat the cream mixture over medium-high heat until just boiling. Remove from the heat; whisk the eggs constantly while gradually pouring the hot liquid into the yolks. Return the egg mixture to the saucepan.
Cook the mixture while stirring constantly with a wooden spoon in a figure 8 motion, over medium-low heat, until thickened, about 5 minutes. When the ice cream mixture is properly cooked it coats the back of the spoon, is satiny thick, and free of any bubbles on the surface. (The ice cream base will taste slightly egg-y.) When the mixture is thickened pull it from the heat; add the reserved 1/2 cup cream, and strain it through a fine strainer into a medium bowl.
Set the bowl of ice cream base in a bowl of ice and whisk until cool. Add the strawberry puree.
Freeze the strawberry mixture in an ice cream machine according to the manufacturer's instructions. (Take care not to over churn the ice cream or it can have a grainy texture.) Place the ice cream in the freezer to set up for at least 1 hour. Serve.
Put the strawberries and the honey in a medium saucepan, and bring to a boil over medium-high heat. Reduce the heat to maintain a simmer; cook, stir frequently, until the berries breakdown and get juicy, about 10 minutes. Remove from the heat and let cool.
Add the lime juice. Taste and adjust the sweetness or tartness of the puree with more honey or lime if needed. Use now, or refrigerate for up to 3 days, or freeze for 1 month.
Yield: about 3 cups
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