Personally , I’d recommend you make your own buns. I whacked out a batch last weekend, only 8 of them, then carefully vac packed them individually ( without taking out enough air so as to squeeze them in any way) then freeze

them.
500g Shipton mill strong white organic flour
350g water
12g salt
5 g of Bio real organic dried yeast
Mix, kneed for 10 mins, let stand until double in size , shape into 8 buns, ( try not to use too much , if any flour in the shaping as it will all add to making you a doughy heavy bun) let rise until double in size .
Bake at 160 deg c until internal temperature reaches 80 deg c ( 10 to 15 mins) then take them out. Don’t worry if they look white and not quite done, they are done, you can give them a blast under the grill if they need to be golden brown. Just don’t dry them out by over cooking them . I bake them in our gas oven or static electric oven depending on what’s not in use at the time. I get great results in both. As stated above , adding some fat, just 25g is enough, by way of butter or lard or beef dripping will add to an even softer more fluffy texture . Sometimes I add fat too , but I normally prefer them without as they get a bit too rich with fat . Fats for winter! The key is not to over cook them, you won’t get a soft white fluffy burger bun to brown in a conventional oven without drying it out and making the crust way too heavy. Secret is to take them out when they have hit 80 deg c internally ( they will look completely under Cooked) you can then give them a milk and olive oil brush just on top , and then 1 minute positioned very close to a screeching hot grill if you want the tops golden brown.
When deploying them I like to cut them open , butter them and toast them on one side ( the butter side ) in a hot skillet and give them a spritz of water from a plant mister bottle while in the skillet, it steams up and adds to their moisture and fluff .
Between Christmas and Easter this year I had to drive through the Netherlands and Germany 20 times, going back and forth between the uk and Germany , I lived off Hamburgers for days on end. I never got bored of them . Burger King beats Mc Donald’s every day of the week in my opinion. Still, whenever I got back home I’d make myself a venison Hamburger.
Own buns, own venison, lettuce tomato, onion, melted plastic cheese slices from Lidl or Id like Brie or sometimes cheddar if I was feeling sneaky, then a sauce using the gastronomic trinity of mustard mayonnaise and Heinz tomato ketchup, topped with a few thin slices of dill pickled Danish Gherkins .
Kindest regards, Olaf