In a small bowl, whisk together 1/2 cup melted butter, 1/4 cup cognac and 1 tbsp thyme. Continue whisking until well combined; set aside.
Place tenderloin on a flat surface and pat dry with paper towels. Fill a Cajun injector with butter-and-cognac mixture and inject in several places. Cover with plastic wrap and store in the refrigerator for at least 2 hours.
When meat is marinated, preheat grill to medium-high (about 400°F). Remove tenderloin from wrap and rub with olive oil and Smoked Salt Steak Rub, pressing firmly so that seasoning adheres well to the meat. Set aside at room temperature.
Meanwhile, heat 1 tbsp butter in a sauté pan over medium-high.
Add sliced shallots and cook for 3-4 minutes or until just tender.
Add oyster mushrooms to pan and cook for 2-3 minutes more.
Add 2 tbsp cognac, and with a spatula or wooden spoon deglaze by scraping up the browned bits from bottom of pan.
Remove from heat and stir in remaining 2 tbsp butter and 2 tbsp thyme. Season mixture with salt and pepper to taste and set aside, keeping warm.
Place tenderloin on grill and cook for 6-8 minutes, each side, for medium rare. Remove from grill and set aside for 3-5 minutes. If you like, you can inject the cooked tenderloin with some of the sauce from the mushrooms and shallots.
Once the meat has rested, slice and serve topped with shallot-oyster mushroom mixture.