Use a fork to lightly mash about one-third of the white beans in a medium bowl. Add kimchi, sesame oil and scallions and stir to combine. Taste and add salt and rice wine vinegar, a little at a time as needed, until the mixture is intensely seasoned. The mixture can be made and stored, covered, in the refrigerator, up to 3 days ahead.
Heat broiler and position an oven rack so it sits 4- to 6-inches below it. Spoon the bean mixture onto the toast slices and spread in a thick, even layer, then top each toast with two slices of cheese. Place toasts on a baking sheet and broil for 2 to 5 minutes, watching carefully to prevent burning, until the cheese is fully melted.
Cut each toast in half and serve.
