Preheat the oven to 350°F. Grease four 4-inch Bundt pans with coconut oil. (Alternatively, grease one 9-inch Bundt pan.) Set aside.
In a large bowl, stir together the water and chia seeds and let sit until gelatinous, about 10 minutes; this will be the chia “eggs.” Meanwhile, in a liquid measuring cup, stir together almond milk and vinegar and let sit for 10 minutes. (By the time the chia “eggs” are ready, this will be ready as well.)
Pour the almond milk mixture into the chia “eggs”; add the yogurt, agave nectar, and vanilla; and whisk together. Sift in both flours, the baking soda, and salt, and stir together, just until well combined. Divide the batter equally among the prepared pans.
Bake the cakes until the tops are browned and a toothpick inserted close to the center comes out clean, 35–40 minutes. Remove from the oven and let cool in the pans for 15 minutes. Invert each pan onto a plate and tap gently to dislodge the cake. (At this point, you can store the cakes in an airtight container at room temperature for up to 7 days.)
Serve the cakes topped with vegan frosting and freeze-dried raspberries, if desired.