Heat the oil in a large pot over medium heat. When it's hot, add garlic, ginger, and Thai red curry paste. Cook, stirring constantly, until it's dark red, about 4 minutes.

Add the chopped sweet potato and stalks of the baby bok choy (the leafy green ends will be added later), broth, coconut milk, fish sauce, 1 teaspoon salt, and 2 teaspoons sugar. Bring the soup to a boil, then reduce the heat to a simmer and cook, uncovered, until the sweet potato is tender, about 7 minutes.

Add the bok choy greens tops to the hot soup, stir to wilt the leaves. Stir in the lime juice and chopped cilantro. 

To serve, divide the cooked rice among four bowls. Ladle the soup over the rice, noodles, then top with chopped cilantro, a wedge of lime, and perhaps a drizzle of sriracha.