Remove the stems up to the leafy part of the collards. Lay each collard leaf, underside up, on a flat surface. Locate the thickest part of the stem and use a vegetable peeler to shave the top off for even thickness (this makes it easier to roll up the leaves).
Fill a large wide skillet or pan with just enough water to coat the bottom. Arrange a few leaves at a time, overlapping, in a circle on the bottom of the pan and sprinkle lightly with salt. Repeat with the remaining leaves.
Put the skillet over medium-high heat and as soon as steam appears, lower the heat to medium, cover and steam until the collards are green, tender and pliable, 5 to 6 minutes. Remove from the heat and use tongs to transfer the leaves to a baking sheet to cool completely.
Whisk together the sour cream, cilantro, 1 tablespoon water, pickled jalapeno and brine in a small bowl. Combine the rice, black beans, tomato and 1/4 teaspoon salt in a medium microwave-safe bowl, cover with plastic wrap and cut a slit in the middle to allow steam to escape. Microwave at 100 percent power until hot, stirring about halfway through, 4 to 5 minutes.
Assemble the burritos: On a work surface, lay out two large leaves side-by-side vertically, slightly overlapped, making a 10-inch wide "wrap". (It's ok if the wrap is not circular.) Form 1/4 of the rice and bean mixture into a log across the leaves about 3 inches from the bottom, leaving a 1-inch border on each side. Drizzle with 1/4 of the sauce, then top with 1/4 each of the avocado and cheese. Fold the sides of the wrap over the ends of the mixture, then roll up tightly from the bottom. Repeat with the remaining wraps and filling. Cut each in half on the bias and enjoy or refrigerate whole for a few hours before serving.
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