In the bowl of a stand mixer, whisk together 4 cups flour, ½ cup sugar, yeast, and salt. Make a well in center and add milk, eggs, and 4 tablespoons melted butter. Beat on medium-low speed with dough hook attachment until dough comes together and is elastic but sticky, about 15 minutes, adding remaining flour a few tablespoons at a time while kneading. (Dough will not pull away from the bowl. It should be sticky but not stick to you when touched with a clean fingertip.)
Transfer for a lightly oiled bowl. Cover tightly with plastic wrap and let rise in a warm place for 45 minutes or until almost doubled in size.
In a small bowl, whisk together cinnamon, cardamom, and remaining ¾ cup sugar. Lightly sprinkle the counter with 2 tablespoons cinnamon-sugar in a 12-inch square. Brush top of dough in bowl with 1 tablespoon butter. Carefully turn out dough, butter-side down, onto sugar; gently pat and stretch into a 12-inch square. Brush top of dough lightly with 1 tablespoon melted butter and sprinkle with 2 tablespoons cinnamon-sugar. Add remaining melted butter to a 15-cup Bundt pan and brush up the sides. Dust with 2 tablespoons cinnamon-sugar, just until lightly coated. (Butter will pool in the bottom of the pan.)
Cut dough into an 8x8 grid. Roll each dough piece into a ball, and coat with additional cinnamon sugar. Place balls in pan as you work. Loosely cover and let rise for 15 minutes.
Preheat oven to 350 while the bread rises.
Meanwhile, combine butter, brown sugar, and up to 2 tablespoons of any remaining cinnamon-sugar in a saucepan over medium-low heat stirring frequently until the sugar and butter start to simmer, immediately remove from heat then whisk together and pour the brown sugar topping over the risen monkey bread. Place pan on a rimmed baking sheet.
Bake for 35 minutes or until top is golden brown and firm to the touch. Let cool for 5 minutes. Invert onto a serving platter and let cool for 10 minutes before serving.