Everything Bagel Seasoning Brioche Monkey Bread

Name: Everything Bagel Seasoning Brioche Monkey Bread
Ingredients: 1 teaspoon active dry yeast; 2 tablespoons granulated sugar; 1/3 cup warm whole milk (105 to 110 degrees F); 4 large eggs; 1 1/4 cups all-purpose flour; 1 1/4 cups bread flour; 1 1/2 teaspoons kosher salt; 2/3 cup (5 1/4 ounces) unsalted butter, cubed, at room temperature; 1 stick (1/2 cup) unsalted butter, melted; 2 cups grated Parmesan; 1/4 cup everything bagel seasoning; 2 cups grated Gruyere; 1 cup (8 ounces) cream cheese, at room temperature; 1/2 cup sour cream; 1 tablespoon chopped fresh parsley; 2 teaspoons chopped fresh dill; Finely grated zest of one lemon plus the juice of 1/2 lemon; Thinly sliced scallions, for serving; Kosher salt and freshly ground black pepper