Melt 1½ tablespoons butter in inner steel pot of pressure cooker set to Sauté on High. Sauté onion in hot butter until onion is softened, about 3 minutes. Press Cancel.
Stir broccoli, vegetable stock, carrots, and celery into onion.
Lock pressure cooker lid in place and set steam vent handle to Sealing. Select Pressure Cook and cook on High Pressure for 1 minute. Let pressure to release naturally for 5 minutes, then turn steam vent handle to Venting to quick-release remaining pressure.
Melt ⅓ cup butter in a saucepan over medium heat. Whisk flour into butter to form a thick paste. Increase heat to medium-high. Slowly pour milk into butter-flour mixture, whisking constantly, until smooth. Cook, whisking constantly, until milk thickens, 2 to 3 minutes.
Add Cheddar cheese to milk mixture and stir until melted.
Stir cheese mixture into vegetable mixture in inner pot of pressure cooker.
Whisk cornstarch and cold water together in a small bowl until smooth.
Select Sauté on High. Pour cornstarch mixture into soup in a steady stream, whisking constantly, until soup thickens to desired consistency, 2 to 4 minutes. Ladle soup into bowls and serve immediately.
