Place the carrots and potatoes into a medium sized saucepan and cover with water so the water is a couple of inches above the veg. Place on the hob and bring to the boil. Boil gently for 10 minutes.
2 medium carrots, 2 small potatoes
Add in the green beans and broccoli, bring back to the boil and continue to cook for a further 2 minutes.
75 g (2.5 oz) green beans, 115 g (2/3 cup) broccoli
Drain out the water using a colander (make sure they're fully dry), then transfer to a bowl.
Gently crush any potatoes you see using a fork. Don't worry if you don't get all of them.
Add the cheese, cream, salt, and pepper to the veg mixture and stir until combined.
Cover the bowl and refrigerate for 1 hour (or up to a day) to firm up the mixture.
Preheat the oven to 220C/425F (fan).
Place the flour, beaten egg, and breadcrumbs into 3 separate shallow bowls. Add the paprika and olive oil to the breadcrumbs and stir together until the breadcrumbs are coated in the oil.
60 g (1/2 cup) plain (all-purpose) flour, 2 eggs, 75 g (1 1/2 cups) panko or homemade breadcrumbs, 3/4 tsp paprika, 3 tbsp olive oil
Remove the mixture from the fridge. Take a good scoop of the veggie mixture (about the size of a large plum) and form into a patty.
Dip the veggie patty in turn into the flour, egg and finally the breadcrumbs, shaking off any excess as you go. Place on a shallow baking tray. Repeat until you’ve used up all of the mixture - it should make 6 patties.
Place in the oven to cook for 20 minutes - until the breadcrumbs are golden and the cheese is just starting to ooze a tiny bit from the burgers.
Remove from the oven and serve on toasted buns with lettuce, tomato, and red onion. Mix together the ketchup and mayo and drizzle on top before placing the tops of the burger buns on the burgers.
6 brioche buns, 12 large lettuce leaves, 2 tomatoes, 1/2 red onion, 3 tbsp mayonnaise, 4 tbsp tomato ketchup
Video
Notes
Can I make them ahead?
You can make the veggie burgers in advance. Simply make them up - including dipping in the breadcrumbs. Then cover and refrigerate for up to a day before cooking. I wouldn't advise freezing the burgers, as potatoes can go watery and a little grainy when defrosting.
Can I make them gluten-free?
Yes, please the panko with gluten-free panko, or homemade breadcrumbs from a gluten-free loaf. Replace the flour with gluten-free plain/all-purpose flour blend
Can I fry them instead of baking them?
Yes, heat 1cm of vegetable oil over a medium-high heat in a large frying pan/skillet until hot. Add the veggie burgers and fry for 4-5 minute on each side until golden brown. They're a little more delicate when frying - so turn them over carefully to ensure they don't fall apart.
Troubleshooting Tips
If your burger looks like it's falling apart in the oven. This can happen for three reasons:
If you leave too much moisture in the vegetables when draining
If you don't refrigerate the veg potato mixture for long enough for the mixture to firm up
If you don't squash the patties into a firm burger shape when shaping them
I've had this happen occasionally (sometimes to one burger out of the batch). If it looks like the burger is falling apart a little, open the oven, carefully push it back together using two spatulas or forks and continue to cook the burger. Squish it together once more when cooked, then place on the burger bun. It may be a little fall-y - apart-y but it will taste great.Nutritional Information is per burger for the veggie burgers only (not the buns, toppings and sauce)