Marinating the chicken: Combine the chopped canned chipotles with 2 tablespoons of the cream. Smear over the chicken breasts, cover and refrigerate for several hours, if time permits, for the chilies to season the chicken.
Finishing the dish: Lay the chicken breasts in a broiler-proof baking dish just large enough to hold them comfortably. Set 6 inches below a very hot broiler and cook until richly brown, 4 to 5 minutes.
Turn the breasts over, drizzle the remaining 1 cup plus 2 tablespoons cream around them and set under the broiler. Cook until the chicken is deep golden and no longer squishy feeling when lightly pressed, 4 to 5 minutes.
Transfer the chicken to 4 warm dinner plates and keep warm in a low oven.
Scrape the cream mixture into a medium-large (3- to 4- quart) saucepan and add the broth and the spinach. Bring to a boil over high heat and cook, stirring nearly constantly, until the spinach is wilted and the cream is reduced and thick, about 3 minutes.
Taste and season with salt, then spoon around the chicken breasts and serve (with rice).
