Ahi tuna and avocado salad on split baguette

Tartine, llesque, smorrebrod, bruschetta.... whatever it’s called, one thing is abundantly clear: The open-faced sandwich is internationally well liked.

Walk through Paris’ St.-Germain-des-Pres and you’re bound to see a glamorous cafe patron lingering at an outdoor table over a gorgeous tartine, maybe piled with slices of ham and topped with a dollop of griotte cherry jam and a big curl of butter, served on a large slice of Poilane sourdough. Traditionally, tartine was prepared for breakfast, spread simply with butter and confiture, but has become chic lunch fare.

And tony llesquerias in Barcelona have elevated what was once a humble repast of day-old bread rubbed with tomato and topped with ham or cheese or possibly anchovies to what is now considered an elegant dinner: crisp, fresh toast layered with arugula, beef carpaccio, paper-thin slices of delicate foie gras and shaved Parmesan.

The combinations are endless, though some are considered classic -- and, of course, classic depends largely on geography. A smorrebrod of gravlax and honey mustard sauce is a Danish favorite. Balzac extolled pork rillettes from Tours for a tartine.

But summer in Los Angeles offers up heirloom tomatoes and wild arugula and fresh figs. And an open-faced sandwich is a perfect summer lunch or light supper -- what better time than mid-August to go uncovered? This isn’t a grab-it-with-your-hands, eat-it-while-you’re-playing-cards Earl of Sandwich-type meal. It’s a refined fork-and-knife entree, each bite to be relished and savored.

Beautiful folds of prosciutto lay atop a bed of wild arugula, with a layer of perfectly ripe heirloom tomato slices peeking from in between. The tomatoes are at their summer height in farmers markets, and heirlooms such as Evergreens or Cherokee Purples or Gold Medals lend their brilliant colors to the sandwich. The leaves of wild arugula are smaller and more tender than the supermarket variety, and any that spill onto the plate form a little salad, which is how tartines are often served -- with a handful of greens on the side.

A balsamic vinaigrette adds bite, and torn basil and a few snipped chives are a final flourish. But for even more richness, add slices of fresh mozzarella or burrata cheese.

On the beach in Tahiti, sidle up to a snack bar for a tuna salad sandwich, and they’ll make it for you with fresh ahi on a crusty baguette. What an idea! -- it’s the inspiration for an open-faced sandwich with ahi tuna grilled until just slightly pink in the center, mixed with Aleppo chile mayonnaise, avocados and Moroccan black olives. Top it with a slice of gently boiled egg, then sprinkle with additional Aleppo chile and fleur de sel.

Start with hearty bread

Bread is the base on which all of your ingredients are layered, so rustic breads or large rolls and baguettes work well. Pa amb tomaquet, bread rubbed with very ripe tomatoes, is the emblematic Catalan dish that often serves as the foundation for llesques, which means slices. Smorrebrod means buttered bread, and a smear of butter before grilling heightens the flavor and texture.

Or use a drizzle of good olive oil. When Majorcans who were imprisoned by Franco during the 1936 civil war staged a hunger strike, their chant went, “Volem pa amb oli,” or “We want bread and oil.”

And bruschetta was once used to check the quality of each season’s olive oil. Rubbing both sides of the toasted bread with a cut clove of garlic also boosts flavor and is great with ingredients such as lampascioni onions, speck, Taleggio and sun-dried tomatoes.

Black mission figs are abundant in markets now. They might not be the first thing you think of when you want a sandwich, but think again. An open-faced sandwich made with figs, caramelized onions and melted manchego cheese is salty-sweet and nutty and warm. Marinating them in a little Muscat de Beaumes-de-Venise or other sweet wine before grilling them gives them a wonderful perfume without adding too much sweetness. The caramelized onions are smoky-sweet and the nutty, salty manchego is a perfect complement. It’s a sandwich that can be lunch and dessert all in one.

But who says you have to limit yourself to just one sandwich? Do like the Danish, who eat smorrebrod in a procession: first one made with fish, followed by one with meat, and finally a cheese smorrebrod.

It’s lunch in Copenhagen -- or Paris or Barcelona or Rome -- on a slice of bread.