Line an 8-inch round cake pan with a large piece of parchment paper and set aside. (The parchment paper fits in the pan easily if you crumple it up beforehand.)
In a small saucepan, combine 2 cups of mulberries (reserving that extra ½ cup of berries), with ½ cup of granulated sugar, and 1 tablespoon of lemon juice. Stir to combine and cook, stirring occasionally, over medium heat for 15 minutes, or until berries have broken down and juices have reduced slightly.
Carefully transfer the compote to a large jar and blend with an immersion blender. (Alternatively, you can blend the compote in a blender.) Set compote aside to cool, reserving ½ cup of the compote in the process.
In a large mixing bowl, whip 2 cups of cold heavy cream to medium-stiff peaks. This can be done with a whisk, hand mixer, or stand mixer. Set whipped cream in the fridge while you continue with the recipe.
Next, in a large mixing bowl, whisk together 12 ounces sweetened condensed milk, 1 teaspoon vanilla extract, and all of the blended compote, saved for the ½ cup you reserved earlier. Mix until well combined.
Gently fold the heavy cream into the flavored ice cream base, being sure not to mix too aggressively to avoid losing the light, airy consistency.
Pour ½ of the ice cream into the prepared pan, and drizzle half of the reserved compote over the top as well as half of the reserved berries. Gently swirl the compote and whole berries into the ice cream.
Top with the remaining ice cream, followed by the rest of the compote and whole berries, again swirling to combine everything. This is how we get beautiful layers of ice cream, compote, and bits of berries all throughout!
Place ice cream in the freezer until solid, at least four hours, or overnight.
Remove ice cream from freezer 5 minutes before serving to make for easier scooping!