Butter a 7 cup oven safe bowl and preheat your oven to 375°F.
Steam the broccoli just until tender, about 5 to 6 minutes after the water under the steamer comes to a boil.
Reserve 2 florets for garnish and transfer the remaining broccoli to the bowl of a food processor fitted with a steel chopping blade.
Melt 1 tablespoon of butter in a small skillet just until it foams.
Add the onion and saute it over medium-high heat until wilted and lightly colored, about 5 to 6 minutes.
Add it to broccoli and process with on/off pulses until fairly smooth, stopping to scrape down the sides of the bowl.
Add the cheeses, eggs, dill, nutmeg, dry mustard, red pepper, salt, and black pepper.
Process just until well blended.
Place 1 phyllo leaf, long end near you, on a clean work surface and brush it lightly with butter.
Fold the phyllo lengthwise in half, then in half lengthwise again, forming a long strip of four layers.
Drape it in the buttered bowl, crossing the center of the bowl and leaving the ends extending over the edge.
Repeat with a second leaf, placing it at right angles to the first.
Use the remaining 6 leaves in the same fashion, covering the entire inside of the bowl.
Scrape the broccoli mixture into the bowl, smoothing it down with the back of a spoon or a spatula.
Turn the ends of the phyllo strips over the filling, starting with the last strip and ending with the first.
Brush with the remaining melted butter.
Bake it on the middle rack of the preheated oven until the top is golden brown, about 40 minutes.
Remove the bowl from the oven and invert it onto an oven-safe platter.
Remove the bowl and return the phyllo dome to the oven until the top is golden brown, about 8 minutes.
Remove and let it stand for 10 minutes.
Then place the 2 remaining florets in the middle of the timbale and present it at the table.