Prep the pan and oven. Preheat your oven to 350°F (175°C).
Generously grease and flour a 10- to 12-cup Bundt pan, getting into every ridge. Tap out excess flour.
Make the blueberry swirl. In a small saucepan, combine blueberries, sugar, lemon juice, zest, and a pinch of salt. Cook over medium heat, stirring, until berries burst and release juices, 5–7 minutes.
Stir in the cornstarch slurry and simmer 1–2 minutes until thick and jammy. Remove from heat, stir in vanilla, and cool to room temperature.
Whisk dry ingredients. In a medium bowl, whisk flour, baking powder, baking soda, and salt. Set aside.
Cream butter and sugar. In a large bowl, beat butter and sugar together until light and fluffy, 3–4 minutes.
Scrape the bowl as needed.
Add eggs and vanilla. Beat in eggs one at a time, mixing well after each. Stir in vanilla.
Combine dairy. In a measuring cup, whisk sour cream and milk until smooth.
Bring the batter together. Add the dry ingredients to the butter mixture in three parts, alternating with the sour cream mixture (dry, wet, dry, wet, dry). Mix on low just until combined.
Do not overmix.
Layer and marble. Spoon about half the batter into the prepared Bundt pan and spread evenly. Dollop half the blueberry mixture over it. Add the remaining batter, then top with the remaining blueberries.
Use a butter knife to gently swirl in a figure-eight pattern 3–4 times. Don’t over-swirl.
Bake. Bake 50–60 minutes, or until a toothpick inserted near the center comes out clean or with a few moist crumbs. If the top browns too quickly, tent loosely with foil in the last 10 minutes.
Cool properly. Let the cake cool in the pan for 15 minutes.
Loosen edges with a thin spatula, then invert onto a wire rack. Cool completely before glazing or slicing.
Optional glaze. Whisk confectioners’ sugar with lemon juice until pourable. Drizzle over the cooled cake.
Let set 10 minutes before slicing.