For the sauce, combine the poblano chiles and heavy cream in a saucepan. Cook over low heat until thickened, stirring frequently. Stir in cilantro and salt. Process in a blender or food processor until pureed. Serve at room temperature.
For the sushi, process the beans in a blender or food processor until pureed. Add the cilantro, cumin, jalapeno chile, salt and pepper. Process until blended.
Grill the chicken over hot coals or broil until cooked through. Cool slightly. Cut into the strips. Steam the spinach until wilted. Coat the tortillas lightly with oil. Heat the tortillas in a skillet just until softened.
Spread the bean puree ¼ inch thick over 1 side of each of the tortillas. Arrange the chicken strips over the bean puree. Place a narrow row of the cheese, spinach, red bell pepper strips, yellow bell pepper strips and carrot over the bottom third of each tortilla. Beginning with the filled edge, tightly roll the tortillas to enclose the filling. Seal the edges of the rolls with the butter. Wrap the tortilla rolls individually in plastic wrap. Chill until serving time. Cut each roll in ¾ inch slices. Serve with the sauce.