The east coast Halifax Donair specialty is something like a gyro, but all beef - no lamb. Rather than the traditional tzatziki sauce, donairs use "donair sauce". For gluten-free, use gluten-free pitas.
Preheat oven to 325 F (160 C). Peel and chop onion, pulse in a food processor until pureed.
Dump onion puree into the middle of 2-3 layers of paper towels or cheesecloth; gather the edges and squeeze all of the liquid from the onions. Return onion solids to the food processor, discard liquid.
Add about 1 lb of the ground beef, the corn starch, spices and salt to the food processor, process until it’s a creamy paste. Add another lb of beef, process again until smooth. Add remaining beef, process once again until smooth, scraping down the sides of the food processor to ensure that everything is smooth. Form meat mixture into a large log shape, place onto a broiling pan/rack. Bake for 2 hours, flipping loaf over at the halfway point.
Once 2 hours are up, remove from oven, allow to cool to room temperature. Wrap cooled loaf in plastic wrap, chill for at least 8 hours, or overnight.
In a medium mixing bowl, combine sweetened condensed milk, vinegar, and garlic powder. Use a whisk to mix together the sauce ingredients - it’ll take some time, but it will eventually come together. Once well combined and hick, transfer to a covered container, chill until use.
To Assemble: Brush pitas with a little water, heat in a hot frying pan until warmed through.
Heat a little vegetable oil in a frying pan. Slice donair meat into 1/4" thick slices, add to pan and reheat until desired texture (If you like the crispy edges, cook a little longer than you would if you don’t!). Pile reheated meat on warm pita, drizzle generously with sauce, top with onions and tomatoes. Wrap in wax paper, parchment paper, or foil to hold it together while eating, serve immediately.