Preheat your oven to 400 degrees Fahrenheit. Prepare a large 9-inch by 13-inch (or equivalent)
Peel the potatoes and cut them in quarters. Place them in the salted cooking water, cover the pot, and cook on high heat (turn to medium-high when the pot begins reaches a hard boil).
Heat a large skillet over medium-high heat and add the olive oil.
Brown the ground beef, adding the onion, garlic, chopped carrots, thyme, paprika, parsley, and salt and pepper just before the beef is cooked through.
Cook over medium heat just until the vegetables begin to soften and the onions become translucent.
Add the wine and cook until reduced.
Sprinkle the flour over the meat mixture and stir well to toast the flour.
Pour in the stock and stir well, adding the green beans (or peas), cooking until the sauce thickens. Remove the skillet from the heat and pour the meat mixture into the bottom of the prepared baking pan.
Drain the cooked potatoes and mash them in the pot along with the butter, milk, and salt and pepper until the mashed potatoes are smooth.
Dollop the mashed potatoes over the top of the meat mixture, smoothing them out completely and creating some grooves with a fork on top of the mashed potatoes (this helps with browning).
Place the baking dish on a baking sheet (it might bubble over the top of the dish in the oven), and bake the Cottage Pie for about 20-25 minutes at 400 degrees Fahrenheit or until the potatoes begin to turn golden brown on top and the filling starts to bubble up around the sides of the baking dish.
Let sit at room temperature for 5 minutes before serving.
Notes
The red wine can be substituted for an equal amount of beef broth (and small splash of red wine vinegar, if desired).