In a heavy bottom pot, add oil and heat over medium heat until hot.
Season chicken with salt and pepper and sear chicken in pot to get a nice golden-brown crust. Don’t worry about cooking chicken all the way.
Remove chicken and add garlic cloves and 2 tbsp butter. When garlic is browning add the thyme and chicken to the pot.
Deglaze with vermouth. Cook until vermouth is almost gone. Add the chicken stock and cover. Let cook on low for 10 minutes.
While chicken is cooking, place potatoes in a medium pot and cover with cold water. Put on medium high heat and cook until potatoes start to fall apart. Strain, crush potatoes and add warmed milk, butter and season with salt and pepper. Mixed thoroughly until smooth.
Mix cornstarch and cold water together to make a slurry.
Remove lid from the chicken pot and add the slurry. Bring to a simmer to let the corn starch thicken the chicken stock.
Now add the cream and reduce until sauce consistency. Adjust seasoning with salt and pepper.
Serve the chicken with the mashed potatoes and plenty of the garlic-chicken sauce.