Peel the green plantains by cutting off the ends and making lengthwise slits through the peel, then remove the skin completely. Cut plantains into 1-inch thick rounds.

Heat vegetable oil in a large skillet over medium-high heat until it reaches 350°F. Carefully add plantain slices in batches, frying for 3-4 minutes per side until they begin to turn golden and are tender enough to flatten.

Remove plantain slices and place on paper towels to drain briefly. Using a tostonera or the bottom of a glass, flatten each piece to about 1/4-inch thickness.

Return the flattened plantains to the hot oil and fry for an additional 2-3 minutes per side until golden brown and crispy. Remove and drain on paper towels, then sprinkle immediately with salt.

While plantains are cooling, heat olive oil in a separate pan over medium heat. Add diced onions and cook until softened, about 4 minutes. Add minced garlic and cook for another minute until fragrant.

Add the black beans with some of their cooking liquid to the pan. Mash the beans with a potato masher or fork while cooking, adding bean liquid as needed to reach desired consistency. Season with cumin, salt, and black pepper.

Continue cooking the beans, stirring frequently, until they reach a thick, creamy consistency, about 8-10 minutes.

To serve, arrange tostones on plates and top generously with the refried beans. Garnish with diced tomatoes, crumbled cheese, and fresh cilantro.

Serve immediately while tostones are still crispy, with lime wedges on the side for squeezing over the top.