Wash the baby potatoes thoroughly and cut them into halves or quarters, depending on their size.
Pour 1 cup of water into the Instant Pot and place the steamer basket inside. Add the halved baby potatoes into the basket. Close the lid and set the valve to 'sealing'. Cook on high pressure for 8 minutes.
After 8 minutes, quick-release the pressure by moving the valve to 'venting'. Once the pressure is released, open the lid.
Add the broccolini on top of the potatoes, close the lid, and cook on high pressure for another 2 minutes.
Perform another quick release. Carefully remove the steamer basket with the potatoes and broccolini and let it cool slightly.
In a mixing bowl, whisk together the mayonnaise, Dijon mustard, red wine vinegar, salt, and black pepper until well combined.
Add the cooled potatoes and broccolini into the bowl and gently fold the mixture together using a large spoon until the vegetables are coated.
Fold in the chopped parsley and cherry tomatoes if using. Adjust seasoning if necessary.
Transfer the salad to a serving dish and refrigerate for at least 15 minutes before serving.