Preheat oven to 375°.
Cut squash in half lengthwise; discard seeds and membrane. Place squash halves, cut sides down, on a baking sheet; bake at 375° for 45 minutes or until tender. Cool. Peel squash. Mash pulp. Set aside 2 cups pulp, reserving remaining pulp for another use.
Combine 2 cups squash pulp, milk, and next 4 ingredients (milk through egg white) in a food processor; process until smooth. Pour into a 1-quart soufflé dish coated with cooking spray. Place soufflé dish in a 9-inch square baking pan; add hot water to pan to a depth of 1 inch. Bake at 375° for 40 minutes or until puffy and set.
While squash is baking, bring 2 quarts water and 1/2 teaspoon salt to a boil in an 8-quart stockpot or Dutch oven. Add Swiss chard; cover and cook 8 minutes. Drain well; toss with butter. Serve immediately.