For the hot sauce: Heat the oil in a medium saucepan over medium heat. Add the garlic and shallots and cook until soft, about 2 minutes. Add the mangoes and habaneros and cook for 5 minutes, stirring often. Add the vinegar and a tablespoon or so of the honey. Bring to a simmer and cook, stirring, until the mangoes are soft, about 10 minutes.
Pour the mixture into a blender and blend until smooth. Add salt, pepper, and more honey to taste. If very thick, thin with a few tablespoons water. Strain through a sieve set over a small bowl. (Makes about 1 cup.)
For the hash: Heat the oil in a large cast-iron skillet over medium-high heat. Add the onions and cook, stirring, until softened, about 3 minutes. Add the jerk chicken, sweet potatoes, scallions and cilantro; toss together. Press the mixture into the pan and cook, undisturbed, until the bottom starts to brown and crisp, about 5 minutes. Turn over parts of the hash, press and crisp again.
For the eggs: Line a plate with paper towels. Crack the eggs into little bowls. Bring a large saucepan of water to a boil over medium-high heat; stir in the vinegar. Slip the eggs into the water, adjusting the heat to maintain a bare simmer. Cook until the egg whites are set but the yolks are still runny, about 4 minutes. With a slotted spoon, transfer the eggs to paper towels to dry.
To assemble: While the eggs are poaching, set a ring mold on a dinner plate and spoon in some of the hash, pressing to crush the potatoes a bit. Remove the mold. Make a little divot in the top of the hash, then spoon on a poached egg and drizzle some hot sauce over the top. (If you don't have a ring mold, just mound the hash onto plates.) Garnish with scallions and cilantro. Repeat for the remaining servings. Serve immediately.
Jerk Chicken Breasts:
In a small bowl, combine the coriander, ginger, brown sugar, garlic powder, onion powder, kosher salt, habanero powder, thyme, cinnamon, cloves and black pepper. Mix to blend. (Makes about 1 cup; extra spice mix can be stored in a sealed container in a cool, dark place for up to 6 months.)
Sprinkle the chicken breasts with salt and pepper on both sides; rub the top side with a generous amount of the spice mix.
Heat the oil in a medium skillet over medium-high heat. Add the chicken breasts, rub-side down, and cook until a crust forms, 3 to 4 minutes. Flip and cook until just cooked through, about 4 minutes more.