Cook blueberries, sugar, and lemon juice in a medium saucepan over medium heat for 5 to 10 minutes. We want them to slightly break down and release some juices.
Remove from heat and cool completely. Refrigerate if you're impatient.
In a large bowl, combine the sweetened condensed milk, vanilla extract, and heavy whipping cream. Whip until soft peaks form.
Fold in the cooked blueberries. Cover with a layer of plastic directly touching the top of the cream. Freeze until solid, 3 to 4 hours.
Oatmeal Cookies
Sift together flour, salt, and baking soda. Set aside.
In a large mixing bowl, beat together the brown sugar, sugar, and butter until fluffy.
Beat in eggs, one at a time, then the vanilla. Stop to scrape the bowl down as needed.
Add the flour mix in 2 or 3 batches, mixing until just combined. Mix in the oats.
Cover the dough and chill for at least 1 hour.
Preheat the oven to 375 F and line cookie sheets with parchment paper.
Roll the dough into walnut sized balls, then place 2 inches apart on the cookie sheets. Gently flatten with a fork or the back of a spoon.
Bake until golden and chewy, about 8 to 10 minutes. 10 to 12 minutes will give you a crispier cookie.
Let cool on baking sheet for 5 minutes before transferring to a wire rack to cool the rest of the way.
Assemble the Ice Cream Cookie Sandwiches
Use a spatula or butter knife to shave the ice cream into strips. Don't worry about making them too thick, you can always put on another layer.
Lay the layers of ice cream onto a bottom cookie until it's as full of ice cream as you'd like, then add a top cookie.