In a mixing bowl, combine heavy cream, whole milk, sugar, and vanilla extract. Mix well.

Add rhubarb compote to the mixture and stir until fully incorporated.

Chill the mixture in the refrigerator for 30 minutes, then churn in an ice cream maker according to the manufacturer's instructions.

Preheat the oven to 350°F (175°C).

In a bowl, cream together softened butter and brown sugar until smooth.

Gradually add flour, baking soda, and salt. Mix until a dough forms.

Drop spoonfuls of dough onto a baking sheet and bake for 10-12 minutes.

Allow cookies to cool completely.

Once the ice cream is ready, scoop a generous amount onto one cookie and top with another cookie to form a sandwich.

Repeat with remaining cookies and ice cream.

Freeze the assembled sandwiches for at least 30 minutes before serving.