Generously butter a 3-quart baking dish (or a 9×13-inch lasagne pan). Toss corn, jalapeño, thyme and scallions together in a medium bowl. Combine cheeses in another bowl. In a large bowl, beat eggs and mayo together, then whisk in milk, salt and 1/2 teaspoon freshly ground black pepper. Spread one-third of bread cubes in prepared baking dish — it won’t fully cover the bottom of dish. Add one-third of corn mixture, then cheese mixture. Repeat layering two more times with the rest of the ingredients, ending with a top layer of corn and cheese. Carefully pour egg mixture evenly over strata (a measuring cup is useful for this). Cover with plastic wrap and refrigerate for at least 8 hours or up to 1 day.