Lemon Layer Cake

INGREDIENTS

• 1/4 cup fresh lemon juice
• 3 1/2 cups confectioners sugar
• 1/2 teaspoon salt
• 1 cup canola oil, plus additional for greasing cake pans
• 2 1/2 cups
• 1 cup milk
• 1 tablespoon finely grated fresh lemon zest
• 3 large egg yolks
• 4 large eggs
• 1 teaspoon xanthan gum
• 1/4 teaspoon guar gum
• 1 tablespoon baking powder
• 1/4 cup plus 2 tablespoons granulated sugar
• 1/4 teaspoon lemon extract
• 2 cups granulated sugar
• 1/2 stick (1/4 cup) unsalted butter, cut into tablespoon pieces
• 2 sticks (1 cup) unsalted butter, softened
• 1/2 teaspoon lemon extract
• 2 teaspoons finely grated fresh lemon zest
• 1 teaspoon vanilla