Heat 1 1/2 tablespoons of oil in a large deep skillet over medium-high heat. Season the chicken on both sides with 1 teaspoon of kosher salt. Add the chicken breasts in a single layer and cook until golden brown, about 4 to 6 minutes. Flip the chicken and cook for an additional 4 minutes. Transfer to a plate and cover with foil.

Lower the heat to medium and add the remaining 1/2 tablespoon of oil to the pan. Add the shallots and 3/4 teaspoon salt, saut? until beginning to turn translucent, about 1 to 2 minutes.

Add the green beans and garlic, tossing until fragrant, about 1 minute. Add the ginger and stir, then add the broth, scraping the bottom of the pan to release any stuck-on bits.

Add the coconut cream and stir to combine. Return the chicken to the pan, nestling it among the green beans. Bring to a simmer and cook, turning the chicken occasionally and stirring the sauce, until the chicken registers 165?F in the thickest parts, about 7 to 10 minutes.

Turn off the heat. Add the lime zest and lime juice, stirring well. Taste and adjust with more juice and/or salt as needed. Top with fresh cilantro and serve with coconut and lime wedges on the side, along with rice, if desired.