While the pasta water is boiling and the pasta cooks, heat a deep sauté pan over high heat and add the olive oil. When it shimmers, add the chicken pieces and sprinkle lightly with salt and pepper. Cook for about 2 minutes, not moving the pieces and letting them brown, then stir and brown the other side. Add the chopped greens, letting handfuls wilt down first if necessary, and cook just until half wilted. Spread in the prepared baking dish (or divide between two dishes). Add the diced shallots and toss.