Preheat the oven to 350°F (177ºC). Grease and flour a 9*13-inch round cake pan.
In a spacious bowl, blend the softened butter and sugar until the mixture becomes light and fluffy.
Beat in the eggs, one at a time, and beating well after each addition. Stir in the vanilla extract.
In another bowl, combine the flour, baking powder, and salt, whisking them together thoroughly.
Gradually add a third of the flour mixture to the butter mixture, alternating with a third of the milk. Repeat until all ingredients are well combined.
Pour the batter into the prepared cake pan and spread it evenly and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
While the cake bakes, prepare the Brown Butter Glaze. In a saucepan over medium heat, melt the butter until it turns brown and emanates a toasty, nutty aroma. Reduce heat to medium-low, whisk in sugar until dissolved. Stir in lemon juice and vanilla extract until the mixture reaches a syrupy consistency.
Once the cake is done, let it cool in the pan for 15 minutes before transferring it to a cooling rack.
Use a skewer to poke holes into the cake, then generously drizzle the Brown Butter Glaze over the top. Allow the syrup to soak in for 5 minutes.
Slice and savor your homemade Maggiano's Butter Cake. It's a rich and indulgent dessert ready to delight your taste buds.