Place the chiles in a small bowl and pour the boiling water over top. Let stand for 15 minutes.
While the chiles are soaking, combine the sugar and 2 tablespoons of the vinegar in a small bowl. Set aside.
Remove the stems from the soaked chiles and transfer them to a food processor. Add the garlic, ginger, 1/2 teaspoon of the salt, the cinnamon, the cumin and the turmeric. Blitz until a thick paste forms. Add a little of the chile soaking liquid if the paste is too thick or too choppy. Transfer the paste to a bowl and set aside.
Place a small saucepan of water over high heat. Bring the water to a boil, then reduce to an energetic simmer. Add the baking soda and, using a spoon, lowered each egg into the simmering water. Cook the eggs for 7 minutes, then transfer to an ice bath. Let sit for 10 minutes. Peel the eggs and set aside.
Heat the ghee or vegetable oil in a large skillet or wok until shimmering. Add the eggs and fry until light golden on each side, roughly 2 minutes a side. Remove the eggs from the wok and cut them in half. Arrange the eggs cut side up on a large platter and set aside.
Add the onions and half of the remaining salt. Reduce the heat and slowly cook the onions until light golden in color and very soft. This should take about 15 minutes.
Add the red pepper flakes and the reserved chile paste to the onions and saute until very fragrant and bubbly. About 5 minutes. Stir in the vinegar/sugar mixture and the remaining chile soaking liquid.
Add the green beans and the last of the salt and cook for 3 minutes or until just tender. Take the wok off of the heat.
Spoon the curry overtop of the sliced eggs. Dress the platter with yogurt, pomegranate arils and fresh mint leaves. Serve immediately with Cumin-scented Rice.