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 cheddar, 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 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 serving.