Step 1

Heat vegetable oil in a large pot over medium heat; cook the onion in the hot oil until soft, 5 to 7 minutes.

Step 2

Drain as much liquid from the onion as possible. Transfer the drained onion to a slow cooker.

Step 3

Place the broccoli, cream of celery soup, cream of mushroom soup, American cheese, and milk into the slow cooker.

Step 4

Cook on Low until the broccoli is tender and the flavors meld, 3 to 4 hours.