For the rice: Bring the water to a boil over high heat in a medium saucepan with a tight fitting lid. Stir in the wild rice and 1 teaspoon of the salt. Adjust the heat so the rice simmers gently, cover, and cook until tender but not mushy, 30 to 35 minutes. Remove rice from heat and let stand, covered 10 minutes. Drain remaining liquid and fluff with a fork.
Meanwhile, mix all the salsa ingredients in a bowl. Set aside, while making the beans so the flavors come together and the sauce gets juicy.
Heat the olive oil in a medium skillet, over medium heat. Add the onion, garlic, and season with the remaining 1/2 teaspoon salt. Cook until the onion is translucent, about 5 minutes. Add the beans and mash them until the mixture is almost smooth but still dotted with bits of bean, adding water as needed to loosen the mash up a bit. Set aside.
When ready to serve the burritos, wrap all the tortillas in a slightly damp towel and microwave until piping hot and pliable, 1 to 2 minutes. (Alternatively, heat a large skillet over high heat until very hot. Cook a tortilla, turning once, until slightly charred and puffy, about 15 seconds per side. Wrap in foil and repeat with the remaining tortillas.) Keep covered while assembling each burrito.
To form the burritos, spoon about a quarter of both the rice and beans and 3/4 cup of the salsa in the center of a tortilla. Top with some of the watercress, if using. Fold the closest edge of the tortilla over the filling, fold in the sides, and then roll the tortilla away from you to form a package. Repeat with the remaining tortillas and filling.
Serve burritos with extra salsa, a dollop of sour cream, and lime, if desired.
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