Fill a 6- to 8-quart pan over high heat with spinach and turn frequently with a wide spatula; add more spinach as leaves wilt and shrink. When all the spinach is added and wilted, in 8 to 10 minutes, cook and stir leaves about 1 minute longer. Pour spinach into a colander to drain. Rinse and dry pan.
Melt butter in pan over medium-high heat. Add onion; stir often until limp, about 5 minutes. Add flour, nutmeg, and thyme. Stir until flour is golden, 1 to 2 minutes. Remove from heat and whisk in broth, cream, and salt until mixture is smooth. Return to heat; stir until boiling, then reduce heat and simmer gently, stirring often, to blend flavors, 5 minutes.
Meanwhile, whirl spinach in a food processor or use a knife to chop coarsely.
Add chopped spinach to the cream sauce. Stir until bubbling. Pour into a shallow 3-quart casserole.
Bake in a 375° regular or convection oven until bubbling at edges, 6 to 8 minutes. Sprinkle with cheese and bake until melted, about 5 minutes longer. Serve hot.