Melt the remaining 4 tablespoons butter and brush the entire inside of pan with it. Line one side of the pan at a time with phyllo: Lay one sheet with the short end in the middle of the bottom of the pan. Drape the rest of the sheet up the side of the pan and over the edge, leaving a good amount of overhang. Brush the section on the bottom of the pan with more butter, then repeat with another sheet of phyllo on the unlined half of the pan, overlapping the sheets a bit in the center.
Sprinkle the phyllo-lined bottom of the pan with remaining Parmigiano Reggiano and season with some pepper. Turn the pan so that one of the draped sides is facing you, and repeat the layering action in the opposite direction leaving you with lots of overhang on all the sides of the pan. Brush with any remaining butter.
With care, transfer the ricotta filling into the phyllo-lined pan; spread it out evenly, from edge to edge, trying not tear the phyllo. Working one at a time, fold each of draped overhang phyllo sheets over the top of the filling, pressing in down gently. Brush each folded-over sheet with a little more butter. Bake 25-30 minutes, until golden brown.
Let cool about 5 minutes, remove the outer ring of the pan and serve.