Pulse salmon chunks in a food processor until chopped but not smooth. (Mixture should be able to hold together to form a patty). Transfer to a bowl, and stir in smoked salmon and dill. Divide mixture into 4 equal pieces. Shape each into a 3 1/2-inch patty (about 3/4 inch thick).
Heat a large nonstick skillet over medium-high heat. Working in 2 batches, toast buns, cut sides down. Transfer to a platter.
Add oil to skillet. Cook patties until golden brown and almost cooked through, about 2 minutes per side.
Spread some mustard onto each bun half. Sandwich half the cress, the burgers, then remaining cress between buns.