Spray 6 inch to 7 inch ( 1 1/2 quart) soufflé dish or round baking dish that fits inside Instant Pot® with nonstick cooking spray.
Whisk cream, eggs, brown sugar, rum, vanilla and salt in large bowl until well blended. Add brioche and half of pecans; stir until blended. Pour into prepared dish; sprinkle with remaining pecans. Cover dish tightly with foil.
Pour 1 1/4 cups of water into pot. Place soufflé dish on rack; lower rack into pot.
Secure lid and move pressure release valve to Sealing position. Press Manual or Pressure Cook; cook at high pressure 35 minutes.
When cooking is complete, use natural release for 10 minutes, then release remaining pressure.
Remove soufflé dish from pot. Remove foil; serve warm or at room temperature. Drizzle with caramel topping, if desired.