Add chicken thighs to a medium sized mixing bowl and season generously with salt and pepper. Then add olive oil, grainy and dijon mustards, garlic powder, and smoked paprika and toss to completely coat the chicken. Let marinate for 30 minutes or as long as you can.
Pre-heat oven to 400 degrees.
Add another few T of olive oil to a large oven safe skillet (I used my cast iron skillet) over medium high heat. When oil is hot, add chicken top side down and cook for 3 minutes. Flip and cook another 2 minutes, then transfer to a plate on the side. *reduce heat if needed and use a splatter screen to keep from getting burnt from oil!
Reduce heat to medium, add butter and allow to melt. Then add garlic, lemon juice, chicken broth, and potatoes and toss to coat. Season potatoes with salt and pepper.
Nestle chicken back into the skillet as best as you can, then top everything with fresh tarragon and lemon slices. Give it all a drizzle of olive oil then pop in the oven to bake for 30-35 minutes, until potatoes are fork tender and chicken cooked through and juicy.