Preheat oven to 400 degrees Fahrenheit (204 degrees Celsius).
Toss cubed potatoes with 1 tablespoon olive oil, 0.5 teaspoon salt, and 0.25 teaspoon pepper on a large rimmed baking sheet.
Pat chicken thighs dry and season with remaining salt and pepper. Arrange chicken among the potatoes on the baking sheet.
Roast for 30 to 35 minutes until potatoes are tender and chicken reaches an internal temperature of 165 degrees Fahrenheit.
While roasting, heat remaining oil in a small saucepan over medium heat; sauté shallots and garlic until translucent, approximately 2 minutes.
Add chicken stock or wine to the saucepan, scraping the bottom to deglaze, and reduce liquid by half.
Reduce heat to low and whisk in heavy cream and Dijon mustard; simmer for 4 to 5 minutes until sauce thickens slightly.
Remove baking sheet from oven, plate the chicken and potatoes, and drizzle with the Dijon cream sauce. Garnish with fresh herbs.