Begin by setting your Instant Pot to the "Sauté" function. Add 1 tablespoon of olive oil and allow it to heat up. Once hot, add the shrimp, kosher salt, and crushed red pepper flakes. Sauté the shrimp for about 2-3 minutes until they turn pink and are just cooked through. Remove the shrimp from the pot and set them aside.
In the same pot, add 1 1/2 cups of vegetable broth (or chicken broth) and bring it to a simmer. Stir in 1/2 cup of quick grits and mix well. Close the lid of the Instant Pot and set the valve to "Sealing." Cook on high pressure for 5 minutes.
Once the cooking time is complete, carefully perform a quick release. When the steam has fully escaped, open the lid and stir in 1 tablespoon of unsalted butter, 1/2 cup of shredded sharp cheddar cheese, and 1 teaspoon of smoked paprika. Mix until the cheese is melted and the grits are creamy.
Finally, return the sautéed shrimp to the pot and stir gently to combine everything. Allow the mixture to heat through for a minute or two, then garnish with chopped fresh cilantro before serving.