Heat pan on medium high heat until smoking. (Make sure area is well ventilated!!) Melt 3 tablespoons of butter in microwave about 20-25 seconds in microwave safe casserole dish. Dredge tilapia fillets in melted butter and season both sides of fillets with blackened seasoning.
Melt remaining 3 tablespoons of butter in preheated pan along with 1/8 cup of extra virgin olive oil (to keep butter from burning). Place fish in preheated pan and cook for 3 to 5 minutes per side. Remove fish and set aside.
In same pan, pour in remaining olive oil and saute shallots and garlic over medium heat for 2 to 3 minutes, or until shallots become tender. Add in jalapenos and cook 1 more minute. Pour in wine and reduce to half; then add in heavy whipping cream. Simmer about 7 minutes or until sauce becomes thick enough to coat the back of a spoon. Add in parmesan cheese and stir. Return fish to pan to warm (about 2 minutes). Serve with Cajun rice.