This one led us on a wild, ahem, goose chase.
We looked in a dozen reference books and the old classic cookbooks, and no one - not Cordon Bleu, not Larousse, not Anne Willan, not Madeleine Kamman, not Julia Child, not Brillat-Savarin, not even Escoffier - has any mention of pheasant under glass. We guessed it was a presentation of roast pheasant in a particular hotel restaurant (though clearly not Escoffier’s) whose name outlived the dish itself.
The new-ish Joy of Cooking makes a reference to pheasant under glass having been "e;the ultimate in upscale dining in an earlier era,": and says it was served under a glass dome to help keep it moist and warm between the kitchen and the table. The book says it was traditionally a roast pheasant stuffed with wild rice and mushrooms. Finally, we came upon a recipe online, supposedly from the Greenbriar Resort, that stated that the pheasant breasts are served under glass to "hold in the cognac flavor that makes this dish so unique." We didn’t actually see cognac specified as the brandy of coice in the recipe, so it seemed a little suspect. Since this question was first answered, we've gotten comments from a number of readers speculating as to the origin of the dish. One person thought the glass should actually be glace, and that it was a pheasant breast en gelée, or covered with a savory gelatin that looked glassy. Another thought the breasts might be basted so much that they developed a glassy sheen all on their own. Finally someone pointed us to Mary and Vincent Price's A Treasury of Great Recipes, and its Pheasant Under Glass recipe from Antoine's restaurant in New Orleans. The recipe in the book was obtained around 1940. Whether it is the original Pheasant Under Glass is anybody's guess - Antoine's had already been in business for a century by then, so it could be a very old recipe.