Select sauté on the Instant Pot and adjust to normal. Add oil to pot. When oil is hot, add shallots and cook for 2 minutes to soften, stirring occasionally.
Add mushrooms, salt, and crushed red pepper; cook for 4 minutes or until mushrooms are tender, stirring frequently.
Add garlic; cook and stir for 1 minute more. Press cancel. Add broth, rice, and thyme.
Secure the lid on the pot. Close the pressure-release valve. Select Manual and cook at high pressure for 6 minutes. When cooking is complete, use a quick release to depressurize.
Add butter and spinach to rice mixture; stir to wilt spinach. Stir in Parmesan cheese.