Special equipment: a large pastry bag or 1-gallon resealable plastic freezer bag
Position a rack in the center of the oven and preheat to 400 degrees F. Line a baking sheet with parchment.
Bring a heavily salted large pot of water to a boil over high heat (the water should be very salty-- even more than the sea). Carefully remove as much of the cauliflower stem as you can without cutting any of the stalk or the florets away. Remove all of the leaves including any small inner ones.
Boil the cauliflower head until it just tender, 6 to 8 minutes. (Take care no to overcook or it will break apart as your stuff it.) Carefully remove the head from the water and allow to drain and cool.
Meanwhile, brush 2 pieces of bread with 1 tablespoon butter each. Cut into 1/4-inch cubes (it's important that the cubes be this small or it will not pipe out of the bag) and transfer to a medium bowl. Finely chop the remaining piece of unbuttered bread and pulse in a food processor until fine crumbs. Add 2 tablespoons butter and the Parmesan, pulse until combined. Transfer to a small bowl and set aside. Wipe out the bowl of the food processor.
Pulse the celery, sage, parsley, thyme, bouillon cube, egg, 2 tablespoons water, 1/2 teaspoon salt and a few grinds of pepper in the food processor until very finely chopped and wet. Fold the vegetable mixture into the bread cubes and stir until smooth and pipeable. Transfer to a large pastry bag (or a 1-gallon freezer bag) and cut a 3/4-inch opening at the tip.
Turn the cauliflower over, stem-side up, and start piping the filling in between the stalks of the florets until you've used about half of the filling. Use your fingers to push the filling down into the holes of the cauliflower. Fill the rest of the cauliflower with the remaining filling. (Use all the filling, even if it looks like the cauliflower is going to explode?it won?t.) Transfer to the prepared baking sheet, stem-side down.
Brush the outside of the cauliflower with the remaining 2 tablespoons butter and sprinkle with 1/2 teaspoon salt. Press the Parmesan-bread crumb mixture evenly over the cauliflower. Bake until the cauliflower is soft and can easily be pierced with a fork and the bread crumbs are a deep golden brown, 40 to 45 minutes. Let cool 10 minutes, cut the cauliflower into wedges, sprinkle with salt to taste and serve.
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