Preheat oven to 350 °F (175 °C). Grease your Bundt pan generously with olive oil or baking spray and lightly dust with flour, tapping out the excess.
In a small bowl, whisk together chia seeds and plant milk. Let sit for 10–15 minutes, stirring once halfway through, until it thickens into a gel.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and all the spices until evenly blended.
In a large bowl, whisk olive oil, sugar, vanilla, and vinegar until smooth. Add the chia-milk gel and whisk until uniform.
Add dry ingredients to the wet in two additions, whisking gently just until no dry streaks remain. The batter will be thick and glossy—don’t overmix.
Pour batter into the prepared Bundt pan and smooth the top. Bake for 35–40 minutes, or until the top springs back and a toothpick inserted into the center comes out clean.
Let cake cool in the pan for 10–15 minutes, then carefully invert onto a wire rack. Cool completely before topping.
Dust powdered sugar lightly over cake, adding in cinnamon or chai spice if preferred.