monkey bread with cream cheese glaze

INGREDIENTS

• 4 tablespoons (1/2 stick or 2 ounces) unsalted butter, divided (2 tablespoons softened, 2 tablespoons melted)
• 1 cup milk, warm (around 110 degrees)
• 1/3 cup water, warm (also around 110 degrees)
• 1/4 cup granulated sugar
• 1 package or 2 1/4 teaspoons rapid rise, instant or bread machine yeast
• 3 1/4 cups all-purpose flour, plus extra for work surface
• 2 teaspoons table salt
• 1 cup packed light brown sugar (CI advises against dark brown, which they feel imparts too strong of a molasses taste; I suspect it wouldn’t bother me)
• 2 teaspoons ground cinnamon
• 8 tablespoons unsalted butter (1 stick or 4 ounces), mleted
• 3 ounces cream cheese, softened
• 3 tablespoons powdered sugar, plus extra if needed
• 2 tablespoons milk, plus extra if needed
• 1/4 teaspoon vanilla extract