Melt the butter in a large saute pan over medium heat. When the butter has melted and looks foamy, add the onion and cook for about 3 minutes, or until softened. Add the kale, salt and pepper to taste and cook, tossing the ingredients frequently, for 3 minutes. Add the cream cheese and mix the ingredients to blend the cream cheese in thoroughly. Remove the pan from the heat and set it aside.

Butter a 9-inch x 13-inch casserole dish. Layer the matzo pieces, cheddar cheese and kale mixture, making two layers.

Whisk the eggs and milk together until well blended. Slowly pour over the strata. Cover the casserole with plastic wrap and chill for at least 4 hours hours or overnight.

About an hour before serving time, preheat the oven to 350 degrees.  Remove the casserole from the refrigerator and bake the casserole for about 45 minutes, or until golden brown.