
Pound chicken breasts to about a 1/2-inch thickness, then season the chicken breasts with salt and pepper.
Heat 1-½ tablespoons olive oil in a large skillet set over medium-high heat.
Add chicken to the hot oil and cook for 5 to 6 minutes per side, or until cooked through and no longer pink. Use an Instant Read Thermometer to check for doneness; chicken is cooked through when internal temperature registers at 165˚F.Remove from pan and transfer chicken to a plate; set aside and keep covered.
Set skillet back over medium-high heat and add in remaining oil.
Stir in chopped shallots and garlic; cook for 1 minute.
Gradually add in chicken broth; stir and scrape up all the browned bits from the bottom of the skillet.
Bring mixture to a boil; continue to boil, gently, for 10 minutes, or until liquid is reduced to about ⅓ cup.
Reduce heat to medium and whisk in the heavy cream.
Add butter, few cubes at a time, stirring after every addition until butter melts. If you want a creamier texture, add the remaining tablespoon of butter.
Stir in 1 tablespoon chopped fresh cilantro, chopped chile pepper, and adobo sauce. If you like, you can add more cilantro.
Taste the sauce for salt and pepper, and adjust accordingly.
Add chicken back into the pan; cook for 1 minute, or just enough to heat through the chicken.
Remove from heat.
Garnish with cilantro and serve with lime wedges.