Heat butter in a large skillet and cook onion until lightly caramelized. Season with 1/2 teaspoon salt and transfer onion to a plate to cool.
Meanwhile, whisk together eggs, milk, parmesan, garlic, thyme, and 1 teaspoon salt in a bowl. Season with pepper. Add bread cubes, and toss well to combine. Toss in onion and speck. Refrigerate, covered, for at least 2 hours.
Spread half the bread mixture on the bottom of a 10 by 14-inch oval baking dish. Sprinkle with 2 cups fontina. Top with remaining bread mixture. Coat a large piece of parchment with cooking spray. Cover strata with parchment, then with foil. Bake for 1 hour at 325 degrees. Uncover, and sprinkle with remaining cup fontina. Raise temperature to 375 degrees and bake until top is golden brown and crusty, 20 minutes or more. Let rest for 15 minutes. Serves 8. (Martha Stewart Living)