Preheat a 4-well waffle maker, then use a brush or paper towel to grease inside surfaces with the olive oil.
Set a wire rack over a sheet pan.
In a medium bowl, whisk the eggs with a pinch of salt. Add the Swiss cheese and caraway seeds and stir to combine. Divide the batter among the 4 wells of the waffle maker and close the top. Cook until the chaffles are golden brown and crispy and the steam has mostly subsided, 5 to 8 minutes. Carefully remove the chaffles and let cool on the prepared wire rack 3 minutes.
Preheat the oven to 350°F (175°C). In a small bowl, whisk together the mayonnaise, tomato paste, mustard, onion powder, hot sauce, Worcestershire sauce, and the salt and pepper. Set the dressing aside.
Top half of the chaffles with 2 slices of pastrami each, folding them to fit. Top each with a slice of Swiss cheese. Bake chaffles on the prepared rack/pan until the cheese is slightly melted, 4 to 5 minutes. Remove from the oven and. Divide the sauerkraut and dressing among the cheese-topped chaffles. Top with the remaining chaffles. Cut each sandwich in half and serve.