Season the chicken breasts all over with 2 teaspoons of the salt and the pepper. Heat the olive oil in a large Dutch oven or braiser over medium-high heat. Once the oil is glistening, add the chicken and cook, undisturbed, until golden brown, about 5 minutes per side. Transfer to a plate.

Add the shallots to the same pot and cook, stirring occasionally, until beginning to soften, 2 to 3 minutes. If the shallots begin to brown too quickly, add a splash of water to deglaze. Add the garlic and cook, stirring, until fragrant, about 1 more minute.

Add half of the kale to the pot and cook, stirring, until wilted, about 2 minutes. Add the remaining kale and cook until wilted about 2 more minutes.

Stir in the heavy cream, Parmesan, mustard, thyme, nutmeg, and remaining ½ teaspoon salt. Increase the heat to medium-high and bring to a simmer. Cook, stirring often, until the sauce is smooth and thickened, about 5 minutes.

Reduce the heat to medium-low and nestle the chicken back into the creamed kale. Add the olives and cook until the internal temperature of the chicken reaches 165°F on an instant-read thermometer, about 15 minutes.

Meanwhile, melt the butter in a small skillet over medium heat. Once the butter is bubbling, add the panko and stir to coat. Cook, stirring constantly, until golden brown and crispy, about 4 minutes.

Sprinkle the toasted panko over the chicken and kale. Serve immediately with additional Parmesan, if desired.