Start by seasoning the chicken thighs with kosher salt and black pepper, then let them rest to dry.
Cut the Yukon gold and purple potatoes into quarters, drizzle them with olive oil, and season with kosher salt and black pepper.
Preheat your oven to 425°F (220°C) and arrange the potatoes on a baking sheet; roast them for about 8 minutes.
Thinly slice the shallot (or onion) and mince the garlic cloves, setting aside half of the garlic and half of the thyme leaves for later.
In a pan over medium heat, add oil and place the chicken thighs skin-side down, cooking for 6-7 minutes on each side until they are nicely browned.
Once browned, transfer the chicken and the partially cooked potatoes to the oven to finish cooking. Keep the oven on, but turn it off when done, allowing everything to stay warm.
Remove any excess fat from the pan, leaving the fond, then add butter and melt it over low heat.
Add the remaining shallot, garlic, and thyme to the pan, sautéing until they soften.
Stir in the flour and cook until there is no raw flour taste left.
Gradually whisk in 1 cup of chicken stock, allowing it to simmer, then add another cup and continue simmering until the sauce thickens.
Lower the heat and let the sauce gently simmer for about 10 minutes, or until it coats the back of a spoon.
In a separate pan, heat olive oil and sauté the asparagus with kosher salt and black pepper for 1-2 minutes.
Add the resting liquid from the chicken pan to the asparagus, then briefly return the chicken to the warm oven.
Stir a couple of tablespoons of chicken stock into the pan, letting it evaporate, then finish with a squeeze of lemon and optional cold butter.
Toss the roasted potatoes with the remaining garlic, thyme, and a splash of olive oil or butter, allowing the residual heat to finish cooking them.
To serve, plate the asparagus, place the chicken on top, and drizzle the gravy over everything.
