Hi there, Jill!
Thanks for bringing your question our way. I'm happy to help.
Your inquiry immediately made me think of the 
Quick-Service dining options at resorts like 
Everything POP Shopping & Dining at Disney's Pop Century Resort, and 
World Premiere Food Court at Disney's All-Star Movies Resort. These locations may have slightly different opening hours, but most are available from 7 a.m. to 11 p.m. daily. 
The options at Disney's All-Star Resorts appear to open a bit earlier at 6:30 a.m., while 
Gasparilla Island Grill at Disney's Grand Floridian Resort & Spa keeps guests fueled daily from 6 a.m. to midnight. Hours are subject to change but you can confirm your specific location's availability using the 
My Disney Experience Mobile App. Simply search the name of your preferred destination using the magnifying glass icon at the bottom of the screen (second from right), or use the location icon (second from left) and select "Dining" from the drop-down box at the top of the screen. 
You can also use your app to place 
Mobile Food & Beverage Orders at many of these locations. Nothing gets the day started quicker than ordering Mickey Waffles in your pajamas and then popping over to pick up your bagged items with minimal wait. My family appreciates the extra few minutes of sleep and prep time on our busy park mornings. 
You might instead be inquiring about the food and dining options at EPCOT World Showcase. Many of these locations typically operate beginning at 11 a.m., but some do have longer hours. We like grabbing a breakfast treat (and a mimosa) from 
Crêpes À Emporter by La Crêperie de Paris, which opens earlier than other locations like Les Vins des Chefs de France, or 
Lotus Blossom Café in China. Again, you can confirm hours specific to each location with the My Disney Experience App, and even get 
transportation or walking directions to any of these destinations.
Jill, I hope this was helpful. If I've misunderstood your question or you need further assistance please come back and let us know.
Magic and memories,
Amy