Heat the oven to 400°F. Spread the goat cheese on the English muffins or bread slices, and top each with a tomato slice. Bake until lightly browned, 5 to 7 minutes.

Meanwhile, put 1½ inches of water in a large saucepan with ½ teaspoon of the vinegar and a large pinch of salt. Bring to a boil over high heat. While the water is heating, combine the oil, the remaining vinegar, the mustard, and the maple syrup in a small bowl or measuring cup. Season with salt and pepper and whisk to combine. Fill a separate medium bowl with cold tap water.

When the water comes to a boil, reduce the heat to medium-low so it simmers gently. Crack the first egg into the water from as close to the surface as possible. (If you’re afraid of burning yourself or breaking the yolk, you can break the egg into a small bowl and then slide it from the bowl into the water.) The white will drift away from the yolk; pull it back by dragging a slotted spoon across the surface of the water. Repeat with the remaining eggs.

Cook the eggs for about 4 minutes, then transfer them to the bowl of cold water with a slotted spoon. (If they stick to the bottom of the pan, dislodge them with a spatula.) Let the eggs cool in the water for 30 seconds, then pull them out with your hand or a slotted spoon and remove any unappetizing strands of white.

Divide the arugula among the toasts, then top each with one of the poached eggs. Drizzle the eggs with vinaigrette and Sriracha sauce, if you like, and serve immediately.