Preheat the oven to 400°F (200°C).
Wash the sweet potatoes; leave the skins on. Prick them a few times with a fork and place on a baking tray.
Roast the sweet potatoes in the preheated oven for about 45 minutes, turning once halfway through, until they are soft when pierced.
Remove the potatoes from the oven and cool until they are safe to handle.
Scoop the flesh from the skins and pass it through a potato ricer or mash thoroughly by hand (do not use a blender). Place the cooked sweet potato flesh in a saucepan.
Add half of the granulated sugar to the saucepan with the sweet potato. Heat over medium–high and cook, stirring continuously, for about 5 minutes until fragrant and the mixture has thickened slightly. Remove from heat and let cool briefly.
In a small bowl, lightly beat the 3 eggs. Stir the beaten eggs into the warm (but not piping hot) sweet potato mixture until evenly incorporated.
Add the remaining granulated sugar, ground almonds, shredded dried coconut, orange zest, all-purpose flour, finely ground cornmeal, and salt to the potato mixture. Stir until you have a thick, sticky, smooth batter.
Let the batter cool completely. Wrap it tightly in cling film and refrigerate for at least a couple of hours or overnight to firm up.
When ready to bake, bring the chilled dough back to room temperature and preheat the oven to 400°F (200°C). Grease a baking tray or line it with parchment paper.
Prepare for shaping: keep a small bowl of water at hand and dip or wet your fingers as needed to prevent sticking. Take about 1 tablespoon of dough and shape it into an elongated oval (broa) and place it on the prepared tray. Repeat, spacing the broas apart to allow for slight spreading.
Lightly beat the large egg yolk and brush each broa with the yolk.
Bake the broas for 15–20 minutes, or until lightly browned on top. The surface may be mottled; this is normal.
Remove the broas from the oven and transfer them to a rack to cool. Serve once cooled to your preference.