As the story goes, an Argentine lady on vacation walked into a beachside restaurant in Punta del Este, Uruguay, and requested a sandwich, specifying it be made with chivito, grilled baby goat, the kind she could get back home.

The chef faced a problem. He had no goat meat in the kitchen, but he wanted to satisfy his customer. Uruguay is, however, home to some of the world’s best grass-fed beef. He quickly grilled a thin slice of steak, then layered it in a freshly baked roll, adding tomato, lettuce and mayonnaise.

Thus the chivito was born. Word spread, and soon everyone was making it. Long story short: This little steak sandwich is now considered the ultimate Uruguayan snack, offered on menus all over the country, and even in Argentina, where it’s known as lomito. Connoisseurs consider it on a par with other iconic sandwiches, like the Philly cheesesteak or the Reuben.

But as I learned while sampling several of them during a recent visit to Uruguay, there are chivitos and chivitos. As with so many other things, there are at least two schools of thought.

At the wonderful beach-side restaurant La Huella, an hour’s drive up the coast from Punta del Este, I had the best chivito ever: smaller than a burger but bigger than a slider. It made an ideal late-afternoon nibble, along with a cold beer or a minty caipirosca. Flavorful and perfectly prepared, it was completely satisfying (but it wasn’t unthinkable to order a second).

At the other end of the spectrum, many places serve artless giant chivitos as big as a plate, piled high with cheese, ham, fried eggs and other add-ons, producing a monstrous overstuffed sandwich that requires a nap later. Nonetheless, this super-size style has its fans.

I consulted the chefs Ignacio Mattos, who was born in Uruguay, and Francis Mallmann, from Argentina, to get their ideas as I worked out a recipe for my own version.

First, the beef must be tender and pounded thin. It can be rib-eye or shell steak, tenderloin or even flat-iron. Two and a half ounces per person is plenty. The bread should be a small kaiser or Portuguese roll, with a crisp exterior but a soft crumb. Lettuce, tomato and mayonnaise are a given, as are a little melted cheese and a slice of hard-cooked egg. Roasted peppers and grilled onions are welcome. A spoonful of chimichurri salsa, freshly chopped, takes it over the top, but nicely.

Chivito Steak Sandwich

Makes 6 servings.

3 5-oz slices tender beef steak, cut 1⁄2-inch thick

Salt and pepper

6 slices pancetta or bacon

1 lg onion, sliced in thin rings

6 thin slices Monterey Jack or mozzarella

6 sm kaiser or Portuguese sandwich rolls, split

1⁄2 C mayonnaise, preferably homemade

Lettuce leaves

6 tomato slices

1 roasted sweet pepper, optional

2 hard-cooked eggs, sliced, optional

Chimichurri salsa (recipe follows)

Ask your butcher for 3 5-ounce steaks, about a half-inch thick, using rib-eye, shell strip or other tender cut. Trim excess fat from edges if necessary. Cut each steak in half crosswise and lightly pound each piece to a 1⁄4-inch thickness. You will have 6 small, thin steaks. Season with salt and pepper.

In a wide cast-iron pan or ridged grill pan over medium high heat, cook pancetta until crisp, about 2 minutes per side. Reserve. Wipe away excess fat and add the onion. Cook, stirring occasionally, until slightly charred and softened, about 5 minutes. Sprinkle with salt and set aside. (Alternatively, grill over hot coals.)

In the same pan (or over coals), sear the beef on one side till nicely colored, about 2 minutes. Flip it and top each little steak with a slice of cooked pancetta, a slice of cheese and some charred onion. Cook for about 1 minute more for rare, 2 minutes for medium rare. Remove steaks from heat.

Slice the sandwich rolls and spread with mayonnaise. For each sandwich, stack lettuce leaves, cooked steak, tomato slice, roasted pepper and egg, if using, and 2 teaspoons chimichurri. Replace the top of the roll and press down lightly. Cut the sandwiches in half if desired. Serve immediately.

Chimichurri Salsa

Makes about 1⁄2 cup.

2 garlic cloves, minced

1⁄2 tsp salt

1⁄2 C chopped parsley

2 tsp chopped fresh marjoram, or 1 tsp dried oregano

1⁄2 tsp red pepper flakes

2 TBS red wine vinegar

1⁄4 C extra virgin olive oil

In a small bowl, stir together all ingredients. May be refrigerated several days but tastes best freshly made.