Heat olive oil in a skillet over medium heat. Season chicken breasts generously with salt, pepper, and mixed herbs. Place them in the skillet, cooking until golden brown on both sides, about 6-8 minutes per side. Remove chicken and set aside.
In the same skillet, add chicken broth and heavy cream. Bring to a gentle simmer, then return chicken to pan, coating with sauce.
In another pot, boil the peeled and chopped potatoes in salted water until tender, about 15-20 minutes. Drain and return to the pot. Add milk, butter, salt, and pepper, then mash until smooth.