Generously butter a 3-quart baking dish and set aside. Heat the olive oil in a large, heavy saute pan over medium heat and add the sausages. Saute until browned and cooked through, about 7 minutes. Remove the sausages to a cutting board and let them cool a bit. Chop the sausages roughly and set aside.
Add the shallots and a generous pinch of salt to the pan. Cook, stirring occasionally, until the shallots are soft, about 5 minutes. (If they start to brown, turn down the heat.)
Add the greens to the pan, along with another big pinch of salt, and cook until they are just wilted but still bright green, 2 to 3 minutes. Set the pan aside, off the heat.
In a large bowl, whisk together the eggs, milk, cream, mustard, and nutmeg, until smooth.
To assemble the strata, spread half of the bread cubes over the bottom of the baking dish. Top with half of the sausage, and then spread half the greens over the sausage and bread. Sprinkle half of each of the cheeses evenly over the greens. Repeat with a second layer of each of the remaining ingredients. Carefully pour the egg mixture over everything in the dish. Cover the dish tightly with plastic wrap and refrigerate overnight, or for at least 6 hours.
Take the strata out of the refrigerator 30 minutes before baking. Heat the oven to 350 degrees F, uncover the strata, and bake it for about 45 minutes, until golden brown and cooked through.