Preheat the oven to 350 degrees F. Liberally spray a 6-cup Bundt pan with nonstick spray.
In a small bowl, whisk together the flour, baking powder, baking soda, and salt.
Add the eggs and brown sugar to the bowl of your electric mixer. Beat on medium speed until fluffy, 3 to 4 minutes. Add the grapeseed oil and beat for 1 to 2 minutes on low speed. Scrape down the sides of the bowl if needed. Add half of the yogurt and the vanilla extract and beat until combined. With the mixer on low speed, add the dry ingredients. Add the remaining yogurt and beat until just combined.
Toss the blueberries with the flour and add them to the batter. Fold them into the batter with a spatula, then pour the batter into the Bundt pan. Bake until the top of the cake is golden brown, 45 minutes. Remove the cake from the oven and let cool in the pan for 15 minutes.
For the blueberry glaze, add the blueberries to a food processor and blend until pureed. Add the powdered sugar, vanilla extract, and milk. Blend until creamy and combined.
Gently invert the pan on a cake plate to remove the cake. As soon as you remove the cake from the Bundt pan pour the glaze over the top.
Note from Jessica: Glazes can be tricky. If your blueberries are juicy, the glaze may need a bit more sugar. If the glaze is too thick, add more milk, 1 tablespoon at a time until it's pourable.