For Filling: Melt 1 tbsp butter in a large skillet over med-high heat. Add onions and thyme, saute until onion is golden, about 5 minutes. Add lamb, saute until coked through, about 6 minutes. Remove from heat, stir in parsley, season with salt & pepper; allow to cool.

For Pastry: Place a sheet of phyllo on work surface with long edge parallel to edge (cover remaining pastry sheets with plastic and a damp towel). Brush sheet with melted butter, top with another phyllo sheet and brush with butter. Top with a 3rd sheet and brush with butter. Cut pastry stack crosswise into 3 rectangles. Spoon to Tbsp of lamb mixture across the short edge of each rectangle, leaving a 2" border at the bottom and 1/2" at the sides. Fold the 2" border over filling, fold in the sides; roll up. Repeat pastry layering, filling and rolling with remaining phyllo and lamb mixture.

Heat oil in a large skillet over med-high heat. Cook lamb rolls in batches until golden on all sides, turning often; about 4 minutes per side. Drain on paper towels and serve warm.