For the crust: Preheat the oven to 350°F. Combine all the crust ingredients together and press the mixture into a 9-inch pie pan, pressing evenly into the base and up the sides. Bake for 10 minutes, then remove from the oven and let cool fully.
For the filling: Place the sugar and water in a heavy-bottomed saucepan or Dutch oven. Bring to a boil and cook while stirring until the mixture begins to turn a deep golden-brown.
While the sugar cooks, whisk the coconut milk together with the salt and cornstarch in a medium bowl until smooth. Set aside.
Remove from the heat and immediately add the oat milk—a few bits of the caramel may harden but whisk rapidly and the heat will melt any hard bits. Continue whisking until smooth and amber-colored.
Add in the coconut milk mixture, whisking until smooth. Return the saucepan to the heat and cook over medium-low heat, whisking constantly, until the mixture thickens slightly and the whisk begins to leave tracks on the bottom of the pot.
Pour the mixture through a sieve into a mixing bowl, pressing with a spatula to remove any lumps (feel free to skip this step if you don’t mind an occasional lump!). Cover with plastic wrap, pressing the wrap gently onto the surface to prevent a skin from forming. Refrigerate the filling for at least 1 hour, or until fully chilled.
Once chilled, remove the filling from the refrigerator and pour it into your baked and cooled pie crust, smoothing the top with a spatula.