• Preheat oven to 375°F.

Make the Chicken:

• Pat dry chicken pieces and season all over with kosher salt and pepper.
• Heat the olive oil in a cast iron (or oven-safe) skillet over medium-high heat. When hot, add the chicken skin-side down and cook until golden brown, about 5 minutes. Set browned chicken aside on a plate (it doesn't need to be cooked through, as it will finish cooking later).
• Reduce the heat to medium. Add the shallots and garlic and cook, stirring, until fragrant, about 1 minute, being careful not to burn.
• Add the grainy mustard and Dijon mustard. Stir to combine with shallots and garlic. While whisking, slowly stir in the white wine and bring to a simmer. Let cook, simmering until the white wine has reduced just a bit, about 2 to 3 minutes.
• Add the butter and let melt, stirring into the pan sauce. Add the thyme and pour in the coconut milk. Stir until well combined and the sauce comes to a gentle simmer.
• Nestle the chicken, skin side up, into the sauce. Transfer into the oven and bake until chicken is cooked through and tender, 35 to 40 minutes.
• Remove from the oven, and let rest for 5 minutes to cool slightly and for the sauce to settle. Finish with more fresh thyme.

For the Cauliflower Puree:

• Meanwhile, while the chicken is cooking, add cauliflower florets into a saucepan with chicken broth, coconut milk, salt, pepper and thyme. Bring to a boil. Once boiling, reduce to a simmer, cover and cook until cauliflower is fork-tender, 10 to 15 minutes.
• Once tender, pour all contents in the saucepan into a food processor or blender and blend until smooth (if you need more liquid, add a few splashes more of broth to the blender). Blend until smooth.

Serve the dish:

• Serve the chicken alongside the cauliflower puree and garnish with thyme leaves, if desired. Enjoy!