Combine the pork, cumin and paprika in a bowl; season generously with salt and pepper and toss. Heat a large pot or Dutch oven over high heat until very hot; add 2 tablespoons olive oil. Add the pork in a single layer and cook, undisturbed, until browned on the bottom, about 2 minutes. Flip and continue to cook, turning, until browned all over, 4 to 5 more minutes; remove to a plate.
Add the remaining 2 tablespoons olive oil, the sweet potatoes, onion, sliced garlic and 1/4 teaspoon salt to the pot. Cook over high heat, stirring, until the onion is softened, about 2 minutes. Add the collards, chicken broth and 1 cup water; cover and bring to a boil. Uncover, reduce the heat to medium and simmer until the vegetables are tender, 8 to 10 minutes.
Reduce the heat to low. Remove 1 cup vegetables with some broth to a blender; add the parsley, grated garlic and 1/4 cup water and puree. Return the pork to the pot and simmer until cooked through, about 2 minutes. Stir in the vegetable puree and warm through; season with salt and pepper. Divide among bowls, top with jalapeno slices and drizzle with olive oil.