Preheat the oven to 375°F. Toss the strawberries with 2 tablespoons of sugar and arrange on a small rimmed baking sheet. Roast for about 8 minutes, until the strawberries begin to soften. Transfer the berries to the bowl of a food processor and blend until smooth. Transfer to a small bowl and chill in the refrigerator.
Pour the heavy cream and buttermilk into a large bowl and place over an ice bath. Place a fine mesh sieve over the bowl.
Combine the milk, remaining ¾ cup of sugar, and salt in a medium saucepan over medium-high heat. Bring the mixture to a gentle simmer. Meanwhile, whisk the egg yolks in a large bowl. Slowly add the warm milk mixture to the egg yolks, whisking until well combined. Transfer the mixture back to the saucepan and cook over medium-low heat for 5 to 10 minutes, stirring constantly, until the mixture is thick enough to coat the back of a wooden spoon. Strain the custard through the sieve and into the heavy cream. Stir for about 5 minutes, until the mixture is cool. Stir in two-thirds of the reserved strawberry sauce and the vanilla extract. Cover the bowl with plastic wrap and chill in the refrigerator for at least 4 hours, or overnight.
Pour the custard into an ice cream maker and process according to the manufacturers’ instructions. Layer the ice cream in an airtight container, alternating the ice cream with the remaining strawberry sauce. Freeze for about 3 hours, until firm.