In a bowl, gently mix the crabmeat with 0.25 cup (about 1 oz / 28 g) of the breadcrumbs, the scallions, mayonnaise, coconut oil, egg white, Dijon mustard, hot pepper sauce, and Old Bay. Use a rubber spatula to keep the mixture light.
Divide the mixture evenly into four portions and shape each into a compact, slightly mounded cake.
Place them on a large plate, cover, and refrigerate for at least 1 hour and up to 8 hours.
Position the oven rack about 6 in (15 cm) below the broiler and preheat the broiler.
Line a rimmed baking sheet with foil and lightly grease it with coconut oil.
Set the crab cakes on the sheet, crumb-side down. Broil until golden, about 12–15 minutes.
Serve immediately.