(Deb Lindsey/For The Washington Post)

A study in contrasting flavors and textures, chiles en nogada may require an explanation. When she first served them at a class at the Mexican Cultural Institute in the District, “People were just baffled,” says cookbook author and public television host Pati Jinich.

The main source of confusion lies in their temperature: The dish is usually served lukewarm — not hot, not cold. The super rich filling stuffed inside a slightly spicy chili pepper and draped in a creamy, lightly sweet sauce might also surprise the eater. But it’s a surprise worthy of exploration. While there are varying origin stories, it is generally agreed that chiles en nogada (“chilies in walnut sauce,” coming from the Spanish word “nogal,” meaning walnut tree) were first made in the Mexican state of Puebla around the time of Mexican independence in 1821.

Featuring the green, white and red colors of the Mexican flag, they are eaten with gusto during the September holiday, but also served for special occasions throughout the year.

The components:

1. POBLANO PEPPER

The mild-to-medium pepper, native to Puebla, is charred and peeled before its seeds and membranes are carefully removed. The stem stays intact, helping the stuffed pepper hold its shape. Once filled, the pepper can also be battered and fried before being adorned with its sauce, a technique called capear, meaning “to give something a cape” or “to cover.”

2. MEAT FILLING

This is where the savory, sour and sweet flavors really shine. The meat-based mixture — often pork, sometimes beef or poultry — typically includes tomato, onion, nuts, Manzanilla olives and various forms of fruit: fresh apple, peaches or plantain; plump raisins; or acitrón (a type of candied cactus) or candied pineapple.

3. POMEGRANATE SEEDS

They provide yet another contrast of texture, giving a welcome burst of fresh, tart juice. (Their presence also illustrates an Old World influence; the fruit was introduced to the New World by Spanish colonists.) Inclusion is mandatory — their color completes the flag.

4. CREAMY SAUCE

It is traditional to use freshly peeled walnuts so the sauce is white and free of bitterness. Pecans can also be used. The nuts are ground with heavy cream and milk; some versions include confectioners’ sugar, cream cheese, goat cheese or a splash of sherry.

Where to try it: The chiles en nogada at Oyamel in the District (401 Seventh St. NW, 202-628-1005) are the best we sampled in the Washington area. They are on the menu from September to early spring, depending on the quality and availability of fresh pomegranates.