Heat a saucepan over medium heat and add the oil. Once hot, add the diced onions, garlic, rosemary, and thyme and cook for 5 minutes until the onions are translucent. Add the diced carrots and cook for another 3-5 minutes.
Meanwhile, place the sliced potatoes in a pot of cold water and bring to a boil. Cool until tender. Once tender, drain well and mash with a potato masher. Heat the cream and 2 tbsp of butter until warm and stir in with the mashed potatoes. Season for salt and pepper.
Add the ground beef and turn the heat to high. Break up the beef and cook until brown. Add the flour and mix until combined.
Add the wine and scrape off any of the crispy bits on the bottom of the pan. Add the stock and simmer for 10 minutes until thickened. Season with salt and pepper.
Salute the peas in a bit of butter just until hot. Season with salt and pepper.
Serve the mince with a side of mashed potatoes and peas.