Preheat oven to 350º F. In a medium-sized bowl, gently stir together the chicken, Monterey Jack Cheese, crema, jalapeños, jalapeño brine, and kosher salt until well combined and set aside.

Spread ¾ cup green enchilada sauce on one half of the bottom of a 13×9-inch baking dish. Spread ¾ cup of the red enchilada sauce on the other half of the bottom of the baking dish, so the sauces meet in the middle. Transfer the remaining green and red enchilada sauces to separate shallow bowls or pie plates. 

Dip one side of one tortilla into the green sauce, letting the excess drip back into the bowl. Lay tortilla dipped side up on a clean work surface. 

Spoon about ¼ cup of the chicken mixture down the center of the tortilla. Roll up tortilla and place seam-side down in the baking dish over the green sauce. 

Repeat with five more tortillas dipped in green sauce, filled, rolled, and placed on the green sauce side of the baking dish. 

Repeat the process with 6 more tortillas, dipped in red sauce, and placed seam-side down on the red sauce side of the baking dish. 

Spoon ⅓ cup of each sauce over the corresponding rolled tortillas.

Bake enchiladas in preheated oven until warmed through, about 20 minutes. Drizzle with additional crema and top with Cotija cheese, radishes, jalapeño slices, and cilantro. Serve remaining red and green sauces on the side.