Heat olive oil in a large pot over medium-high heat; cook and sir onion and red bell pepper until softened, 6 to 8 minutes. Add garlic, curry, ginger, and cayenne pepper to onion mixture; cook and stir until evenly coated, about 30 seconds.
Mix vegetable broth, tomatoes, Granny Smith apple, quinoa, and currants into onion mixture; bring to a boil. Reduce heat to low, cover pot, and simmer until quinoa is tender, 15 to 20 minutes. Stir cilantro into soup and season with sea salt and pepper.