Place potatoes in a large pot of salted water, bring to a boil, and cook for 15-20 minutes until fork-tender. Drain and mash with butter and milk until smooth.
Season chicken thighs with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Sear chicken skin-side down for 8 minutes until golden and crisp; flip and sear for 2 minutes, then remove from pan.
Lower heat to medium, add minced garlic and sundried tomatoes to the skillet, and cook for 1 minute until fragrant.
Whisk in chicken broth, heavy cream, parmesan, oregano, and red pepper flakes. Bring to a light simmer.
Return chicken thighs to the skillet, skin-side up. Simmer uncovered for 12-15 minutes until sauce thickens and chicken reaches an internal temperature of 165°F.
While chicken simmers, sauté asparagus in a separate pan with a touch of oil and salt over medium heat for 5-7 minutes until tender-crisp, finishing with lemon juice.
Platter the chicken over a bed of mashed potatoes, pour remaining cream sauce over the meat, and serve with asparagus and fresh basil garnish.