Preheat the oven to 325°F. Prepare a 9-inch springform pan by wrapping the outside with heavy-duty aluminum foil.
Place the oats, sugar, and salt in the bowl of a food processor and process until fine but slightly textured. Add the butter and pulse until the mixture is crumbly. Add the crust mixture to the springform pan and use a cup or flat-bottomed glass to press the crust into an even layer and about 1 inch up the sides.
Bake for 10 minutes until lightly golden brown. Remove from the oven and set aside.
Rinse out the food processor. Add the cottage cheese and process until smooth, then add small pieces of the softened cream cheese and sugar, continuing to process on low speed until creamy and fully combined, about 3 minutes. Add the cornstarch, vanilla, and lemon juice, mixing until just incorporated.
Add the eggs one at a time, processing briefly after each addition until just combined, scraping down the sides of the bowl as you go. Remove the blade and use a rubber spatula to stir the mixture to remove any air bubbles.
Pour the filling into the prepared oat crust. Place the cheesecake in a large roasting pan and carefully pour boiling water halfway up the springform pan.
Bake 60–70 minutes, until the edges set and the center jiggles slightly.
Turn the oven off and prop the door open slightly, letting the cheesecake slowly cool down for about 1 hour. Then, remove the pan from the water and oven, remove the foil, and place it on a wire rack to cool completely. Once cooled to room temperature, cover with plastic wrap and refrigerate for at least 8 hours or overnight.
Gently run a knife around the edges of the pan and carefully release the ring of your springform pan. Run the knife between the crust and bottom pan and use a spatula to carefully lift the cheesecake to a serving plate.
For the blueberry compote: Add the blueberries, sugar, water, lemon juice, and vanilla to a small saucepan over medium heat. Simmer for about 15 to 18 minutes, stirring occasionally, until the blueberries soften and the mixture thickens. Remove from heat and let cool; it will continue to thicken and turn jammy as it cools.