Preheat the oven to 350°F.
Grease a 10-inch springform pan thoroughly and set it aside.
Place the chopped Vidalia onions and 1/2 cup butter in a large skillet.
Sauté the onions over low heat for approximately 10 minutes, stirring occasionally, until the onions are softened.
Add the poppy seeds, salt, paprika, and black pepper to the softened onions.
Stir until the onions are evenly coated with the seasonings.
Remove the skillet from the heat and set the onion mixture aside.
In a large mixing bowl, combine the all-purpose flour, cornstarch, baking powder, and brown sugar.
Stir until the dry ingredients are evenly mixed.
Cut 1 1/4 cups cold butter into the dry ingredients until the mixture forms a loose, crumbly texture.
Melt the remaining butter and allow it to cool slightly.
In a separate mixing bowl, whisk together the eggs, whole milk, sour cream, and melted butter until smooth.
Make a well in the center of the dry ingredients.
Pour the wet mixture into the well.
Stir gently until the batter is just combined. Do not overmix.
Transfer the batter to the prepared springform pan.
Spread the batter evenly in the pan using a spatula.
Spoon the seasoned onion mixture evenly over the top of the batter.
Bake for 35 to 45 minutes, or until a knife inserted into the center comes out clean.
If the top begins to brown too quickly, loosely cover the cake with foil during the final minutes of baking.
Remove the cake from the oven and allow it to cool for at least 5 minutes.
Run a thin knife around the edge of the pan if needed.
Carefully release the springform pan.
Slice the cake into wedges and serve warm.