In a medium saucepan, combine the chopped rhubarb, 1/2 cup granulated sugar, water, and lemon juice.

Bring the mixture to a gentle simmer over medium heat, stirring occasionally. Reduce heat to low, cover, and cook for 15-20 minutes, or until the rhubarb is very tender and has broken down. Mash gently with a fork if desired for a smoother texture. Remove from heat and let cool completely. Transfer to an airtight container and refrigerate for at least 1 hour, or until thoroughly chilled.

In a clean medium saucepan, combine the whole milk, heavy cream, 1/2 cup of the granulated sugar (from the 3/4 cup total), and a pinch of salt. Heat over medium heat, stirring occasionally, until the sugar dissolves and the mixture just begins to simmer around the edges (do not boil). Remove from heat.

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

Gradually temper the egg yolks by slowly pouring about half of the hot milk mixture into the egg yolk mixture, whisking constantly to prevent scrambling. Pour the tempered egg yolk mixture back into the saucepan with the remaining hot milk mixture.

Return the saucepan to low heat. Cook, stirring constantly with a wooden spoon or spatula, until the custard thickens enough to coat the back of the spoon (it should reach about 175-180°F or 80-82°C on an instant-read thermometer). Do not let it boil.

Immediately remove the custard from heat and strain it through a fine-mesh sieve into a clean bowl to remove any cooked egg bits and ensure a smooth texture. Stir in the vanilla extract.

Cover the custard directly with plastic wrap to prevent a skin from forming and refrigerate for at least 4 hours, or preferably overnight, until thoroughly chilled.

Once both the rhubarb compote and custard base are thoroughly chilled, churn the custard in your ice cream maker according to the manufacturer's instructions. This usually takes about 20-30 minutes, until it reaches the consistency of soft-serve ice cream.

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

Cover the container tightly and freeze for at least 4-6 hours, or until the ice cream is firm. Let it soften at room temperature for a few minutes before serving for the best texture.