Combine strawberries, rhubarb, 1/2 cup granulated sugar, and lemon juice in a heavy-bottomed saucepan. Cook over medium heat, stirring occasionally, until the fruit breaks down and the mixture thickens, about 15-20 minutes. It should resemble a chunky jam.

Remove from heat and let cool completely. Once cool, transfer about 1 cup of the compote to a separate bowl and mash it with a fork or pulse briefly in a food processor for a smoother texture. Keep the remaining chunky compote as is. Chill both portions in the refrigerator for at least 2 hours, or until very cold.

In a medium saucepan, combine heavy cream, whole milk, 3/4 cup granulated sugar, and salt. Heat over medium heat, stirring occasionally, until the sugar dissolves and the mixture just begins to simmer around the edges. Do not boil.

While the cream mixture heats, whisk the egg yolks in a separate medium bowl until light yellow and slightly thickened.

Slowly temper the egg yolks: gradually pour about 1 cup of the hot cream mixture into the whisked egg yolks, whisking constantly to prevent the eggs from scrambling. Then, pour the tempered egg yolk mixture back into the saucepan with the remaining hot cream.

Continue to cook over low to medium-low heat, stirring constantly with a spatula, until the custard thickens enough to coat the back of a spoon (about 170-175°F or 77-79°C). Do not let it boil.

Remove from heat and stir in the vanilla extract. Pour the custard through a fine-mesh sieve into a clean bowl to remove any potential bits of cooked egg. Place plastic wrap directly on the surface of the custard to prevent a skin from forming. Chill in the refrigerator for at least 4 hours, or preferably overnight, until completely cold.

Once the ice cream base and both portions of compote are thoroughly chilled, churn the ice cream base in your ice cream maker according to the manufacturer's instructions, until it reaches the consistency of soft-serve.

During the last 5 minutes of churning, gradually add the mashed strawberry rhubarb compote to the ice cream maker, allowing it to incorporate evenly.

Transfer half of the churned ice cream to an airtight freezer-safe container. Dollop half of the chunky strawberry rhubarb compote over the ice cream. Swirl gently with a knife or spoon. Add the remaining ice cream, then dollop the remaining chunky compote and swirl again.

Cover the container tightly and freeze for at least 4-6 hours, or until firm, before serving.