Prep the aromatics: Finely mince the garlic. Finely chop the carrot, celery, and onion.
Cook the aromatics: In a large dutch oven or heavy pot, add 2 tablespoons of oil and the garlic. Heat to medium-low, then cook the garlic until it just starts to get fragrant, about 1 minute. Stir in the red pepper flakes; once they sizzle, add in the onion, carrot, and celery. Increase the heat to medium and cook the aromatics until softened and slightly shrunken in size, about 8 to 10 minutes. Season with salt and pepper.
Blend the roasted red peppers: While the aromatics are cooking, use a small blender to blend the drained peppers into a smooth and homogeneous paste.
Build the rest of the soup: Add the roasted red pepper paste to the pot, and stir to combine. Let cook for about 3 to 4 minutes, until the paste begins to stick to the sides of the pan. Stir in 1 teaspoon of the smoked paprika, cumin, and coriander, and cook for 1 minute. Add in the apple cider vinegar, vegetable broth, 1 1/2 cups water, and 1/2 cup of farro. Season with salt and pepper (though keep in mind, the feta garnish will add some more saltiness). Bring to a boil, then reduce the heat and simmer until farro is just barely al dente, about 20 to 25 minutes.
Finish the soup: Just before the farro is cooked, stir in the chickpeas. Continue simmering until farro is completely cooked, about 5 minutes. Stir in half the parsley into the soup. Taste the soup, and adjust with seasonings, adding the remaining paprika if desired, and additional amounts of the other spices as needed. If the soup is too thick, you can thin it out with a bit of water.
Serve the soup: Divide the soup into bowls, and top with feta crumbles and more parsley. Note: Once served, the soup is best when you mix in the feta, so that you can get a bit of saltiness in each bite. Serve hot with crusty bread or pita.