In a pot of boiling water, cook the potatoes until very soft. Drain and mash with a potato masher; set aside.
In another pot of salted boiling water, cook the carrots for about 5 to 6 minutes. Remove carrots from the water and drain. Add the turnips and cook for 6 to 8 minutes. Remove the turnips and drain. Add the leeks, cook for only a couple of minutes, remove and drain.
In a small bowl, combine the soft butter, mustard, herbs, salt and pepper. Mix well.
In a large pot, bring 1 1/4 cups of water to a boil. Add the carrots, turnips, green beans, and garlic. Boil for a couple of minutes, and add the mashed potatoes and remaining vegetables. Stir and simmer on low for 2-3 minutes, then remove from the heat and add the butter mixture. Stir well until the mix is completely incorporated.
When ready to serve, poach the eggs. Serve the “ragout” in individual bowls, place a poached egg on top, and sprinkle with grated Parmesan. Serve immediately.
Chef's Tips
You can use silken tofu instead of poached eggs. Don’t prepare this dish in advance as it will lose its freshness. It’s best to cook it 30 minutes before serving. The mustard, herb and butter mix can also be used as a dip for fresh spring radishes.