Turn on the Instant Pot and select Sauté, adjust to More or High, based on your Pressure Cooker.
Once its Hot add butter and melt it. Once melted, add the onion, garlic, carrot, and celery, and cook, stirring occasionally, until tender, about 5-7 minutes.
Add wild rice, salt, pepper, red pepper flakes, Italian herbs and dried parsley to the pot and stir for 1 minute.
Add chicken broth and chicken, stir to combine.
Close and lock the lid, point the valve to sealed, and select High Pressure, for 5 minutes, press Start.
When the cook time ends, turn off the pressure cooker and allow the pressure to release naturally for 10 minutes, then a quick pressure release.
When the valve drops, carefully open and remove the lid.
In a small bowl, mix the cornstarch with the water until fully dissolved.
Press on Sauté and adjust it to Low, add the cornstarch mixture and stir.
Add cubed cream cheese, and stir until melted.
Add half and half, stir, but do not bring to a boil. Season with additional salt and pepper to taste and turn off the IP.
Serve with croutons or crusty bread, and garnish with fresh parsley.