Cook almonds in a large skillet over medium heat, tossing occasionally until fragrant and crisp, about 7 minutes. Remove from heat. Once almonds have cooled, place in a food processor and process until finely ground; set aside.
In the same skillet, heat 1 tablespoon oil over medium-high. Add onion and cook, stirring constantly until tender, about 4 minutes. Working in batches, add greens, season with salt and pepper, and stir to combine. Cover for 1 minute to steam, then add remaining greens. (Depending on the size of your pan, you might need to do this in a few batches, steaming one until wilted and then adding another.) Uncover and cook 1 to 2 minutes until greens are tender and water has evaporated. If water remains in pan, drain, and cool greens to room temperature.
In a small bowl, combine ground almonds, garlic, and remaining 2 tablespoons oil; season with salt and pepper.
Spread a teaspoon or so of almond mixture on each slice of bread. Top with a slice of cheese. Toss greens with vinegar and place on top of the cheese.