Preheat oven to 425°F.
Pulse thyme, flour, Parmesan, milk, butter, eggs, sugar, salt, and pepper in a blender or food processor until smooth.
Place a 10-inch nonstick ovenproof skillet in oven for 5 minutes.
Carefully remove skillet from oven and add batter.
Return to oven and bake until puffed and golden brown, 20-25 minutes.
Serve with crème fraîche, smoked salmon, baby greens, and lemon wedges if desired.
