In a 5- to 6-quart pan, blend polenta, chicken broth, 1 cup water, and evaporated nonfat milk. Stir over high heat until mixture boils, then reduce heat and simmer, stirring often, until polenta is smooth to taste, about 15 minutes. Stir in the shredded parmesan cheese, minced fresh chives or green onions, sage, and salt and pepper to taste.
While polenta cooks, in a deep bowl, with a mixer on high speed, whip 4 large egg whites until they hold soft peaks.
Remove polenta from heat and stir in 2 large egg yolks and about 1/3 of the whipped egg whites, then fold in remaining whites.
Meanwhile, rinse 6 portabella mushroom caps (4 1/2 to 5 in. wide) and pat dry. Rub tops lightly with olive or salad oil (about 2 teaspoons total). Lay caps, gill side down and side by side, in a 10- by 15-inch pan. Broil 4 to 6 inches from heat until mushrooms begin to ooze juice; turn them over and broil until flexible when bent, 8 to 10 minutes total.
Rinse and core tomato; cut tomato crosswise into paper-thin slices.
Lightly oil a shallow 3-quart (9- by 13-in.) casserole. Arrange mushroom caps, gills up, in a single layer in casserole; pour mushroom juices around caps. Spread spoon bread in an even, solid layer over mushrooms. Arrange tomato slices on spoon bread.
Bake in a 375° oven until spoon bread is well browned at the edges and lightly browned on top, about 40 minutes (about 30 minutes in a convection oven). Cut spoon bread and mushrooms into servings. Transfer to plates with a wide spatula.