First of all, decide whether you want to peel the yams ahead of time. I like to cook them with the peel, and then it comes off easily after the slices are cooked. For the beet, just scrub well, or peel, it’s up to you.
Preheat oven to 400º. Mix 3 tbsp. of the olive oil with the herbs and garlic, add some salt & pepper, and mix. Immerse each slice of yam in the oil on both sides until coated, and place in a Dutch oven or ceramic roasting pot with a fitting lid.
Follow this with the beets. Place some of the thyme and rosemary stems over the vegetables. Place the lid on top and roast covered for 45 minutes. If you don’t have a Dutch oven or roasting pot, you can wrap the yam slices together in foil, and the beets together in a separate foil pouch. The idea is to lock in the moisture and flavor. Meanwhile, make the ragout.
Place the vegetable broth in a small sauce pan on low heat and dissolve the arrow root in the broth. This will be the thickening agent for the ragout.
Put the remaining olive oil in a sauce pan, add the shallots and begin to brown the shallots. Add the mushrooms and sautée until they become tender. Turn up the heat, add the optional wine and deglaze, stirring up any caramelized bits until the wine is evaporated. Add the tomatoes, Dijon mustard.
Add the vegetable broth with arrow root. Simmer until it becomes a silky, gravy-like consistency (but much silkier and smoother than traditional gravy). Taste for salt & pepper.
When the vegetables are ready, remove from the oven, peel yams if necessary, and assemble your stacks by placing first a yam slice, then some mushroom ragout, then a beet slice, then more mushroom ragout, and then a second yam slice. Top the stack with a finishing touch of more ragout. Repeat until your four stacks are assembled.
Garnish with a little chopped parsley or a rosemary sprig. Enjoy with a simple spinach and radicchio salad, rice, or quinoa.