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Say ‘‘mushroom mille-feuille’’ to most veteran cooks and eaters, and they will most likely picture a golden mound of puff pastry filled with wild mushrooms in cream and herbs — a fine dish, if old-fashioned and increasingly rare.

This is nothing like that.

Early this summer, I was steered by the elbow to Dirty French, the newest New York restaurant from Rich Torrisi and his partners. Their first, Torrisi Italian Specialties, a reimagining of Italian-American classics, opened in 2009 on Mulberry Street. Dirty French, which opened in the fall of 2014 on Ludlow Street, handles sort-of-classic French food in a similarly playful manner.

And that’s where I was commanded by my dinner companion to order the mushroom mille-feuille: ‘‘It’s the best thing on the menu,’’ he insisted. I wasn’t sure what would be placed before us, but I certainly wasn’t expecting this: layers of paper-thin mushroom slices, seasoned, buttered, pressed in a pan and chilled for a day, then sliced and seared and served with a piquant sauce.

Think of the best pommes Anna, but with the firm, chewy texture of good mushrooms, perfectly crisped and graced with a colorful purée. It’s not literally a mille-feuille, which translates as ‘‘a thousand leaves,’’ but more like 50 or 75 layers. The sauce, which on my first visit was a green curry made with ramps, is neither irrelevant nor lily-gilding, though the mille-feuille itself is so enticing that just a little soy sauce and lemon would complement the mushrooms’ earthiness well.

Simple as it sounds, this dish was the most interesting thing I’d eaten in months. The next morning, I was on the phone with Torrisi, asking him if the mille-feuille was too complicated for us — that is, for you and me, ordinary home cooks. ‘‘With a little patience, anyone can do it,’’ he said. Soon I was in the Dirty French kitchen, where Torrisi, along with Dai Matsuda, the chef de cuisine, greeted me with a huge pile of sliced king trumpet mushrooms and a pot of melted butter. In their hot and busy kitchen, we went to work, buttering, salting, layering and repeating.

Nose around for borscht recipes, and you’ll find that most classic hot borschts call for beef stock or a beef or veal shank to simmer along with the vegetables.

I wanted to make a lighter, vegetarian version of hot borscht. But I also wanted my soup to have the kind of depth of flavor that a meaty backdrop provides, without overpowering the winelike, heady flavor of the beets.

So, as I often do when faced with this kind of challenge, I turned to mushrooms.

I made a strong broth by soaking dried mushrooms, and combined that with a red-beet-and-garlic broth that was the result of simmering beets with sliced garlic for 30 minutes. I used shiitakes for my broth one time, and porcinis another. The shiitake broth is a bit lighter, with more of a mineral edge to it; I like them both.

There are lots of fresh mushrooms in this soup as well. You can use regular white buttons or creminis. They’re sliced and cooked in olive oil with onion, carrots, celery and garlic, then simmered with the beets in the combined beet-and-mushroom broth.

Make sure to buy your beets with the greens attached, the more generous the bunch the better, as you’ll be adding the leaves to the soup toward the end of its simmer, making it all the more heady, healthy and satisfying.