Heat the oven to 220 C / 425 F. Line a large rimmed baking sheet with parchment paper.
Rinse the bream inside and out, then pat completely dry with paper towels, including the cavity.
Stuff each cavity with lemon slices, a rosemary sprig, a bay leaf, and a pinch of cracked pepper.
In a large bowl, mix the coarse salt with the egg whites and water until it looks like wet sand and clumps when pressed.
Spread a 1 cm bed of the salt mixture on the tray, place the fish on top, then pack the rest of the salt over and around each fish to fully encase it, pressing firmly to seal any gaps.
Bake for 25 to 28 minutes, until the crust is golden and firm, and an instant-read thermometer inserted through the crust near the spine reads 135 F / 57 C.
Remove from the oven and let rest 8 to 10 minutes, this lets the crust firm up before cracking.
Crack the crust with the back of a spoon, brush off the loose salt, peel back the skin, and lift the fillets away from the bone.
Serve warm, drizzled with olive oil and lemon wedges on the side.