Unfortunately, the concept of an 'open sandwich' is not consistent with the English language definition of 'sandwich'. In a Swedish owned bar, I was recently offered the choice between a bowl of soup with crusty bread for £4.50 and, as a special deal, a bowl of soup with a salmon sandwich for £7.00. I chose the latter, and the soup came on the same plate as a small piece of bread with a bit of salmon and mayonnaise on top. The barman treated me somewhat dismissively when I inquired after the whereabouts of the second piece of bread !!
During the Middle Ages, thick slabs of coarse bread called "tranches" (late 15th century French) or, in its English derivative, "trenchers", were used as plates. At the end of the meal, the food-soaked trencher was eaten by the diner (from which we get the expression "trencherman"), or perhaps fed to a dog or saved for beggars. Trenchers were as much the harbingers of open-face sandwiches as they were of disposable crockery.
As such, open-face sandwiches have a unique origin and history, differing from that of the (multi-slice) sandwich.
A condiment, such as mayonnaise, or mayonnaise-based dressing is also often included in some form. An old traditional replacement for butter on a piece of bread with herring is pig fat. There are many variations associated with the smørrebrød/smørbrød/smörgås and there are even special stores, cafés and restaurants (especially in Denmark) that specialize in them.
The Dutch and Flemish Uitsmijter consists of one or more slices of bread topped with fried eggs (one per slice of bread), and can be accompanied by slices of cheese and/or meat (roast beef or ham). The dish is often served as a hearty breakfast. Sweet toppings are commonly used for breakfast in the Netherlands and Belgium: e.g. sprinkles, vlokken, or muisjes, next to the more widespread peanut butter, honey, jam, and chocolate spread.