To cook the rice, combine the parsley, cilantro, poblanos, onion, garlic, 1/2 teaspoon salt, and black pepper in a blender with 1 3/4 cup water. Blend on high until smooth. Allow the mixture to sit for a few minutes. This will separate the liquid from the foam. Discard the foam that has settled at the top, and set the green liquid aside.
Set a medium saucepan over medium-high heat with the oil. Once hot, add the rice and cook until toasted and lightly golden brown, stirring often, about 5 minutes. Season with the remaining 1/2 teaspoon salt. Pour the verde liquid into the hot pot and cook until the water has absorbed into the rice. Cover tightly with a lid, lower the heat to as low as it'll go and cook the rice until tender, about 15 to 20 minutes.
In the mean time, to make the white refried beans, set a medium skillet over medium-high heat with the oil. Once hot, add the onions and garlic and sauté until soft and just beginning to brown. Stir in the beans along with the water in the can. Season with salt and pepper, and low the flame. Let simmer for about 5 minutes and then mash everything together with a potato masher until smooth. Keep warm on the side over low until ready to use.
Fill a large skillet with about 1-inch of oil and set over medium-high heat. Once hot, fry the small tortillas on both sides until golden brown and crunchy, about 3 to 4 minutes in total. Transfer to a baking sheet lined with paper towels, and while hot season with a bit of salt on top. Fry the tortillas in batches until they're all crispy. In a small bowl, mash together the avocado, with the juice of 1 lime juice, salt and pepper.
To assemble the tostadas, spread the crispy tortillas with some of the refried white beans, top with verde rice, and then sprinkle with lettuce, avocado, tomato, pickled jalapeños and cheese. Serve warm or at room temperature. Enjoy!