How to Make It
Butter a 9x9-inch pan and set aside.
Melt 2 tablespoons of butter in a large frying pan while you slice the onion and the dill stems, roughly chopping and reserving the dill fronds, and setting aside. Add the onion, dill stems, and a pinch of salt to the butter and sauté over medium-low heat until soft and fragrant (but not brown). Put the onions in the 9x9-inch pan and return the frying pan to the heat.
Add the remaining tablespoon of butter, melt, add the bread cubes, and increase the heat to medium-high. Stir every few minutes, so that the cubes toast lightly on all sides. Add the toasted cubes to the pan on top of the onions.
Beat together the eggs and the milk and season with salt and pepper. Pour over the bread and use your (clean!) hands to press the bread down into the custard. Cover with foil and refrigerate for at least one hour and up to a day.
About an hour and a half before you’d like to eat, remove the strata from the fridge and let it sit out while you preheat the oven to 350° F. Set the foil off to the side while you dollop the crème fraiche over the top of the strata, spreading it around gently; sprinkle the chopped dill on, and top with lots of black pepper. Sprinkle with a few caraway seeds if you like. Put the foil back on and bake the strata, covered, for 45 minutes; then remove the foil, increase the heat to 400° F, and bake uncovered for 10 minutes more, until slightly browned on top. Let sit 5 minutes or so (while you run around refilling coffee cups) before slicing into it. Top with more fresh dill to taste.