Cook the linguine in a large pot of salted water until al dente. Reserve about 1 cup of pasta water, then drain.
Season the steak with Cajun seasoning, smoked paprika, black pepper, and salt. Heat the olive oil in a heavy skillet over medium-high heat and sear the steak until browned with crisp edges and cooked to your liking.
Add 1 tablespoon butter and half the garlic. Toss the steak briefly in the garlic butter, then transfer it to a plate to rest.
Melt the remaining butter in the skillet. Add the rest of the garlic, then stir in the heavy cream, milk, and cream cheese until smooth.
Remove from the heat and melt in the Monterey Jack and Parmesan. Toss with the linguine until every strand is well coated, adding pasta water only if needed. Serve beside the steak and finish with parsley.