Heat oven to 400 degrees and line a baking sheet with parchment. Brush your halved spaghetti squashes with 1 tbsp olive oil (inside and outside), then sprinkle with salt and pepper. Bake 30-40 minutes. Remove from heat and cool until you can comfortably handle the squashes. Then, take a fork and scrape the squash tendrils out of the skin until only a thin but still-sturdy foundation of squash skin remains. This is your boat! Place the spirals into a bowl and set aside.
Heat 2 tbsp of olive oil over medium in a large stockpot or Dutch oven. Whisk flour into oil until fully incorporated, then add leeks, onions, thyme, and garlic. Cook for 2-3 minutes until leeks and onions are translucent and the mixture is fragrant. Pour in stock or water and potatoes. Bring to a boil, then lower to a rolling simmer and cook potatoes 8-10 minutes until potatoes break when penetrated with a fork. Add oat milk, salt and pepper to taste.
From here, you have two options. If you own an immersion blender (which I recommend anyone get, they're phenomenal!) simply submerge and whip the soup until no large chunks remain and the mixture is uniform. If you do not, carefully transfer 1-2 cups at a time into a traditional blender until the whole batch is creamy.
Throw spaghetti squash noodles into the soup and stir with a wooden spoon until combined. Ladle soup into squash boats and top with additional thyme, salt and pepper as desired.