Place the mussels and water in the Instant Pot. Lock the lid and set the valve to sealing.
Cook on high pressure for 1 minute, then quick-release the pressure, keeping hands and face clear of the steam.
Discard any mussels that stay closed. Remove the meat from the shells and set aside.
Preheat the oven to 450°F.
Heat 1 tablespoon of the olive oil in a skillet over medium-high heat. Add the Brussels sprouts and cook for 5 to 6 minutes, until browned at the edges.
Add half the garlic and cook for 30 seconds more. Remove from heat.
Roll out the flatbread dough on a floured surface and transfer to a baking sheet. Brush with the remaining olive oil.
Bake the plain flatbread for 8 minutes, until just starting to set and lightly golden.
Remove from the oven and spread with ricotta mixed with the remaining garlic and a pinch of salt. Top with the Brussels sprouts, shelled mussels, mozzarella, and Parmesan.
Return to the oven and bake for 6 to 8 minutes more, until the cheese is melted and bubbling and the crust is golden. Scatter with fresh thyme and serve with lemon wedges.