In a food processor, blitz the mince, lentils and half the cornichons and onions with a pinch of black pepper until combined. On a large sheet of greaseproof paper, use clean hands to divide the mixture into four equal pieces and pat out into 15cm rounds. Put a 30cm non-stick frying pan on a medium-high heat. Grate the cheese, finely slice the remaining cornichons and onions with the pepper, then divide it all between the rounds, placing in the centre of each. Pull the meat up and over the filling, pinching to seal, then gently pat and shape into 3cm-thick patties. Brush with olive oil, then cook in the hot pan for 1 minute on each side. Brush with mustard and cook for another minute, then flip and repeat, nudging the patties towards the edge of the pan to sear the sides, too.
Halve the buns and sit the burgers inside, then – and this is the key to this dish – chop each burger in half and retoast the cut sides for a final 30 seconds, until golden, gnarly and cooked through, before serving. Great with a fresh green salad.