Brush melted butter into a 9-inch deep-dish pie pan or a 10-inch cake pan. Layer phyllo sheets evenly into the pan, buttering as you go. Allow the phyllo to overhang the edges of the pan by 5-inches. Cover completely with a damp towel to prevent phyllo from drying out; set aside.
Drain the kale and press it between paper towels to remove excess water. Cook the sausage in a large skillet over medium high heat, stirring often, about 5 minutes or until sausage crumbles and is no longer pink. Remove from skillet and place on a paper towel-lined plate to absorb excess grease.
Preheat oven to 350°F. In a large saucepan over medium-high heat, bring broth, cream and salt to a boil. Gradually whisk in grits and return to a boil. Reduce heat to medium-low, cover and simmer, whisking occasionally, for 10-12 minutes or until thickened.
Remove from heat and stir in 1 cup cheddar, and 3/4 cup of the sharp cheddar, and pepper. Stir until melted.
Gradually mix in about 1/4 of the grits into the eggs to temper. Return egg mixture to the pot of grits. Stir in kale and sausage until well blended.
Spoon the grits mixture into phyllo-lined pan. Fold and scrunch overhanging dough over the edges of the quiche leaving the center exposed. Brush phyllo edge with more melted butter. Sprinkle remaining 1/4 cup grated sharp cheddar onto the center of the quiche.
Bake for 40-50 minutes or until set. Remove from oven onto wire rack, and cool slightly before