Rich Coffeecake with Sweet Cheese Filling

INGREDIENTS

• 2 envelopes (4½ teaspoons) instant yeast
• ¼ cup warm water (about 110 degrees)
• ½ cup (3½ ounces) granulated sugar
• 4 large eggs
• 2 tablespoons milk
• 1 teaspoon vanilla extract
• 4¼ cups (21¼ ounces) unbleached all-purpose flour
• 1½ teaspoons salt
• 16 tablespoons (2 sticks) unsalted butter, cut into 1-inch pieces and softened but still cool
• 8 ounces cream cheese, softened but still cool
• ¼ cup (1¾ ounces) granulated sugar
• 2½ tablespoons all-purpose flour
• Pinch salt
• 2 teaspoons finely grated zest from 1 lemon
• 1 large egg
• ½ teaspoon vanilla extract
• 1/3 cup packed (2-1/3 ounces) light or dark brown sugar
• 1 tablespoon granulated sugar
• ½ cup (2½ ounces) all-purpose flour
• ½ teaspoon ground cinnamon
• ¼ teaspoon salt
• 5 tablespoons cold unsalted butter, cut into 8 pieces
• ¾ cup (3 ounces) confectioners' sugar, sifted
• 3½ teaspoons milk
• 1 teaspoon heavy cream (preferably) or whole milk