Combine chopped rhubarb, quartered strawberries, 1/2 cup granulated sugar, and lemon juice in a medium saucepan. Bring the mixture to a gentle simmer over medium heat, stirring occasionally.

Continue to simmer for 10-15 minutes, or until the rhubarb is very tender and the fruit has broken down into a jam-like consistency. Remove from heat and stir in 1/2 teaspoon vanilla extract.

Transfer the compote to a shallow bowl and let it cool completely to room temperature, then refrigerate until thoroughly chilled (at least 2 hours).

In a medium saucepan, combine the heavy cream, whole milk, 1/2 cup of the granulated sugar (reserving the remaining 1/4 cup for the egg yolks), and salt. Heat over medium-low heat, stirring occasionally, until the mixture is hot and steaming, but not boiling. Remove from heat.

In a large mixing bowl, whisk the egg yolks with the remaining 1/4 cup granulated sugar until light in color and slightly thickened.

Slowly temper the egg yolks by gradually whisking about 1 cup of the hot cream mixture into the egg yolk mixture. This prevents the eggs from scrambling. Once tempered, pour the egg yolk mixture back into the saucepan with the remaining hot cream.

Return the saucepan to medium-low heat and cook, stirring constantly with a spatula or wooden spoon, until the custard thickens enough to coat the back of a spoon (about 5-8 minutes). Do not boil.

Immediately strain the custard through a fine-mesh sieve into a clean bowl to remove any potential cooked egg bits and ensure a smooth base. Stir in 1 teaspoon vanilla extract.

Cover the bowl with plastic wrap, pressing it directly onto the surface of the custard to prevent a skin from forming. Refrigerate until thoroughly chilled, at least 4 hours, but preferably overnight.

Once both the ice cream base and the compote are completely chilled, churn the ice cream base in your ice cream maker according to the manufacturer's instructions, typically for 20-30 minutes, until it reaches a soft-serve consistency.

Transfer about half of the churned ice cream to an airtight freezer container. Drop spoonfuls of the chilled strawberry rhubarb compote over the ice cream. Repeat with the remaining ice cream and compote.

Gently swirl the compote into the ice cream with a knife or spoon to create a marbled effect, being careful not to overmix. Smooth the top.

Cover the container tightly and freeze for at least 4-6 hours, or until the ice cream is firm.