I’m the kind of cook who goes to the market with a list and returns with everything but what was on it. It takes only one beautiful squash, apple or bunch of herbs to make me change my plans. Even when I’m at the stove, there’s no guarantee that I won’t turn things topsy-turvy at the last minute. It’s what happened over and over with this recipe, and I’ll be surprised if you don’t end up playing around with it, too.

The inspiration for the dish is hachis Parmentier, the French version of shepherd’s pie. For the classic, the base is chopped beef (“hachis” means minced) and the top, the Parmentier part, is mashed potatoes. In the culinary lexicon, Parmentier always signals potatoes, an homage to Antoine-Augustin Parmentier, who championed the nutritiousness of spuds in late 18th-century France, his native land, where farmers were forbidden to grow them for fear that they caused leprosy.

I can imagine celebrations in the streets of Paris when, in 1772, the Faculty of Medicine declared the white potato edible. And I can imagine hachis Parmentier being created just minutes later, because it’s one of the tastiest ways to make a meal out of leftovers or inexpensive cuts of meat.

My version of the Parmentier depends less on leftovers and more on what’s in the fridge. The core ingredients are the chicken – I use thighs, but you can use other parts – and the sausage: chicken (my choice) or pork, spiced or plain. The chicken is not hachis-ed, but cut into morsels, and the sausage is broken up, so you get different textures in the dish. As for the vegetables, here’s where the tinkering takes off. I’ve given you a recipe for a medley using onion, carrots, parsnips, celery and kale or spinach, but if you’ve got something else or want to keep adding vegetables, I say do it.

Recently, I made this dish with the standards plus cubed turnips (they added a nice bitterness to the mix), cubed butternut squash, leeks (left over from soup) and bottled chestnuts (they’d been lurking in the cupboard since Thanksgiving). I used chard and curly kale, because that’s what I had, and I was tempted to add fennel, but I was in danger of a pot-runneth-over crisis.

As for the spices, I started using garam masala with this dish when a friend gave me some. From there, it was just a hop, skip and jump to adding curry powder, turmeric for color and star anise because I’m crazy about it. But the chicken-vegetable-and-potato combo would take to fresh herbs. Think parsley, thyme, bay leaf and maybe even a little tarragon; to tagine-like spices such as cinnamon, ginger and saffron; or to something American Southwest spicy, such as chili powder, a jalapeño and maybe a drizzle of honey to soften it all.

And then there are the potatoes. I went contra-Parmentier and used sweet potatoes, but if you prefer whites, hey, it’s your dish. And if, like me, you can’t resist running with an idea (sorry, Michael), do what I’ve often done: Cook celery root along with the sweets, and mash them together.

Tinker. Fiddle around. Have fun.

Greenspan is the award-winning author of 11 cookbooks, the most recent of which is Baking Chez Moi. Read more on her Web site, doriegreenspan.com, and follow her on Twitter: @doriegreenspan.