Preheat your oven to 350°F (175°C). Thoroughly grease and flour a 10-cup bundt pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
In a large bowl with an electric mixer, beat the softened butter and granulated sugar on medium-high speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Reduce the mixer speed to low. Add the flour mixture in three parts, alternating with the champagne in two parts, beginning and ending with the flour. Mix just until combined; do not overmix.
Pour the batter evenly into the prepared bundt pan. Bake for 35-40 minutes, or until a wooden skewer inserted into the center comes out clean.
Let the cake cool in the pan on a wire rack for 15 minutes. Then, carefully invert the cake onto the rack to cool completely.
Once the cake is cool, prepare the glaze. In a small bowl, whisk together the powdered sugar and 3 tablespoons of champagne until smooth. Add more champagne, one teaspoon at a time, to reach a pourable consistency.
Drizzle the glaze over the top of the cooled cake, letting it drip down the sides. Let the glaze set for about 20 minutes before slicing and serving.