Peel and dice the Yukon Gold potato, then place in a pot of boiling water for 12-15 minutes until tender.
Season the chicken breast evenly on both sides with sea salt and black pepper.
Heat 0.5 tsp of ghee in a stainless steel or cast iron skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes per side until the internal temperature reaches 165°F, then remove and let rest on a plate.
While chicken cooks, steam the green beans for 5 minutes until bright green and crisp-tender.
Drain the potatoes and mash them with 0.5 tsp of ghee and a splash of chicken broth until smooth.
In the same skillet used for the chicken, add the remaining 0.5 tsp of ghee and sauté the minced garlic, rosemary, and thyme for 1 minute until fragrant.
Whisk the arrowroot powder into the remaining chicken broth until dissolved, then pour the mixture into the skillet.
Simmer the sauce for 2-3 minutes, stirring constantly, until it thickens into a glossy gravy.
Plate the mashed potatoes and green beans, slice the chicken, and pour the herb gravy generously over the chicken and mash.