Preheat your oven to 375°F (190°C). On a parchment-lined baking sheet, toss the fresh strawberries with granulated sugar and lime zest until evenly coated. Roast in the oven for 20 minutes, stirring halfway through, until they are caramelized and tender. Let them cool for a few minutes, then puree the strawberries in a blender or food processor until smooth.

In a medium saucepan, combine heavy cream, whole milk, and half of the granulated sugar. Heat this mixture over medium-low heat, stirring gently until warm but not boiling. In a separate bowl, whisk the egg yolks with the remaining sugar until pale and thick.

Gradually mix in the warm cream to temper the yolks, ensuring a smooth custard base.

Return the tempered yolk mixture back to the saucepan and cook it over low heat, stirring regularly until the mixture thickens and coats the back of a spoon, about 5-7 minutes. Be careful not to let it boil. Once thickened, strain the custard through a fine-mesh sieve into a clean bowl to remove any solids.

Add the chopped fresh basil leaves to the warm custard and steep for 15 minutes to infuse the flavors.

After steeping, remove the basil leaves from the strained custard. Stir in the roasted strawberry puree, freshly squeezed lime juice, additional lime zest, and vanilla extract, ensuring everything is well combined.

Cover the mixture and chill in the refrigerator for at least 4 hours, or until completely cold.

Once chilled, pour the mixture into an ice cream maker, following the manufacturer's instructions. Churn until it reaches a soft-serve consistency, which will typically take about 20-25 minutes.

Transfer the churned ice cream into an airtight container, smoothing the top with a spatula. Cover the surface with parchment paper or plastic wrap to prevent ice crystals.

Place the container in the freezer for at least 4 hours, or until the ice cream is firm and scoopable.

When ready to enjoy, scoop the delightful Roasted Strawberries & Lime Basil Ice Cream into bowls or cones. Garnish with fresh basil leaves, a drizzle of strawberry syrup, or a slice of lime.