Season the main item (chicken, fish or vegetable) with kosher salt, coating the item well on both sides.
Melt the butter in a wide bottomed pan over medium-high heat. Cook until the butter is browned and has a roasted, nutty aroma.
Pat the main item dry and place in the pan, presentation side down, and sear until well-browned. Flip and brown well on the second side. Remove the item from the pan to rest on a rack.
Add the shallots and garlic to the pan and sauté for 3 to 4 minutes until lightly browned.
When the shallots and garlic are golden and fragrant, scatter the herbs and flour into the pan. Cook, stirring often, for 1 minute more. Gradually whisk the milk into the pan and bring the mixture to simmer. Add the lemon zest, salt, pepper, and nutmeg.
Add your main ingredient to the pan, and add more milk to cover if needed. Bring the milk in the pan to a light simmer; you are looking to maintain a temperature around 180˚F (82˚C). Cook until proper doneness is reached: boneless chicken, about 20 minutes; fish filets, 12 to 15 minutes; vegetables, 15 to 20 minutes.
Remove the items from the pan rest on a rack. The poaching liquid may be reduced to create a sauce if desired:
- For chicken, add thinly sliced mushrooms and simmer until tender and thickened.
- For fish, reduce until thickened, then remove from the heat and stir in capers, lemon juice, and dill.
- For vegetables, reduce until thickened, then remove from the heat and stir in ground chiles, sliced cilantro, and lime juice.