Put salmon in a food processor and pulse until chopped to medium coarse, two to three 1-second pulses. Take care not to overprocess. There should still be some chunky pieces; you don't want a completely smooth puree.
In a medium bowl, lightly beat the egg. Add the salmon and combine with a rubber spatula. Add mustard, lemon zest, hot sauce, 1 1/2 tsp kosher salt, and 1/2 teaspoons pepper. Mix until well combined. Cover bowl with plastic wrap and chill for at least 30 minutes or up to 4 hours.
Remove salmon mixture from refrigerator, turn it out onto a baking sheet, and portion into eight equal mounds. With wet hands, gently shape each mound into a 2 1/2" wide patty. Sprinkle each patty with a pinch of the thyme on each side.
Heat olive oil in 12" nonstick skillet over medium-high heat. Add salmon cakes and reduce heat to medium. Cook the cakes, turning once, until nicely browned on both sides and interior is no longer raw, 5-6 minutes total cooking time. Be careful not to overcook the cakes. Transfer to a plate and cover to keep warm.
Can make bite size cakes for appetizers:.
Portion mixture into 24 small mounds (about 3/4 oz. each), shape into small cakes and cook until nicely browned on both sides, 3-4 minutes total.