In a small bowl, stir together the mustard and honey. Using a food processor, pulse the salmon to finely chop. Place in a bowl and season with salt and pepper. Add 2 tablespoons of the honey mustard, the chives, Old Bay and lemon zest. Form into 4 large burgers. Drizzle some EVOO into a large nonstick skillet or griddle, add the burgers and cook, turning once, over medium-high heat for 6 minutes for medium-rare, 10 to 12 minutes for medium-well.
Lightly butter the english muffins. Top each muffin half with the salmon burgers, remaining honey-mustard sauce, the sliced cucumbers and onion and the cress. Eat these patties with a knife and fork.