Cut the spaghetti squash in half crosswise. Place cut-side down in a large slow cooker and cook on high for 2 to 3 hours or low for 4 to 6 hours. The squash is cooked when it can easily be squeezed.

Turn off the slow cooker and remove the squash. Add the butter and garlic to the slow cooker and let the butter melt.

Meanwhile, use a large spoon to scoop the seeds out of the spaghetti squash. Discard. Scoop the flesh out of the skin and add back into the slow cooker. Add the asiago, parmesan, salt, and pepper and toss to combine all the ingredients. Spread out evenly over the bottom of the slow cooker.

Sprinkle with mozzarella and replace the slow cooker lid. Let sit in the warm slow cooker until melted, another 10 minutes or so. Sprinkle with fresh basil and serve.