Put the potatoes and carrots together in a large pot, cover with water by 2 inches and boil until the potatoes are soft.
Meanwhile, heat the olive oil and 2 tablespoons butter in a large skillet, add the onions and saute over medium-low heat until brown and caramelized
When the potatoes are cooked, drain well. Add them along with the carrots back into the pan and shake over a low flame to dry them out; then add the remaining butter and mash them, adding cream or half and half as necessary to make a soft mashed potato. (The carrots will likely remain in pieces you can see, this is fine and how it should be). Stir in the caramelized onions.
In a small sauté pan, add the butter and panko, cook over low heat until the breadcrumbs are toasty. Sprinkle over the mashed potatoes and serve.
If making for a dinner party: Coat 8 ramekins with softened butter, then coat with breadcrumbs. Spoon the potato mixture into the ramekin, smoothing out the tops. (Make-up to 2 days in advance, cover with plastic wrap and put in the refrigerator).
When ready to serve, remove the ramekins from the refrigerator and place on a cookie sheet. Remove the plastic from the tops and place in a hot 375°F oven for about 30 minutes or until hot. Gently run a knife around the edge of the ramekin, then using pot holders, turn the timbale out onto the plate, shaking gently to release.