In the bowl of a stand mixer, combine water, sugar and yeast. Allow to sit until foamy, about 5 minutes. Add in melted butter, flour and salt and, using the dough hook attachment, knead for about 5 minutes or until dough is slightly sticky and has completely pulled away from the sides of the bowl.

Shape dough into a ball and place in a large lightly greased bowl. Cover with plastic wrap and let rise until doubled, about 1 hour.

Meanwhile, roast the broccoli: Preheat oven to 400 degrees F. Toss broccoli with olive oil, salt and pepper and place in a roasting pan. Roast until lightly brown and slightly crunchy, about 20-30 minutes. Remove from oven and set aside to cool. Keep oven on at 400 degrees F. Line two baking sheets with parchment paper and set aside.

When dough is nearly doubled, prepare the water bath: Bring water and baking soda to a boil in a large stockpot.

When dough is doubled, remove from bowl and place on a lightly floured surface. Divide dough into 8 equal pieces and roll each piece into a ball. Flatten each ball into an 8-inch long circle. Place some cheddar, then some ham, then some broccoli in the center. Fold one end of the circle over to the other end to form a half moon; pinch ends tightly to seal. Repeat with each piece of dough.

Using a slotted spoon, carefully lower one calzone at a time into hot water bath and boil for 30 seconds, flipping over halfway through. Remove from water bath and place on prepared baking sheets.

Repeat with each calzone. Brush calzones with egg wash and sprinkle with salt. Bake 12-15 minutes or until calzones are a deep golden brown. Remove from oven and cool slightly before serving.