For the cake:
1 1/2 cups sugar
1 cup unsalted butter
1 tablespoon vanilla extract
4 large eggs
2 cups all-purpose flour
For the vanilla glaze
3 tablespoons butter, melted
1 cup powdered sugar
2 teaspoons vanilla extract
2 to 3 tablespoons milk
8x4 inch loaf pan
Preheat oven to 350°F. Butter and line an 8-inch loaf pan with parchment paper, creating a sling.
In a large bowl with an electric hand mixer or in the bowl of a stand mixer, beat sugar, butter, and vanilla extract on medium high speed until light and fluffy, about 8 minutes. Scrape down the bowl. Beat for another 30 seconds.
Add eggs one at a time, waiting until each egg is fully incorporated and scraping down the bowl before adding the next egg.
With the mixer on low speed add in the flour and mix just until a batter is formed, but you still see some streaks of flour. Use a spatula to finish folding the dough together. It should be thick.
Scoop the batter into the prepared loaf pan and smooth the top. Bake for 60 to 70 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Remove the cake from the oven. Run a thin knife around the edges while still warm, then cool for 15 minutes in the pan before unmolding. Allow to cool completely on a wire rack.
Whisk together the melted butter, sugar, and extract. Add the milk 1 tablespoon at a time until the glaze is a smooth, pourable consistency.
Pour the glaze over cooled cake. The cake can be served immediately, or you can wait for the glaze to dry, then cover with plastic wrap and store on the counter for up to 5 days. The cake can also be tightly in plastic and frozen for up to three months.