Preheat your oven to 350°F (175°C).
Grease and line two 9-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt.
In another bowl, mix the plant-based yogurt, plant-based milk, vegetable oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined.