Heat oil in a large saute pan, preferably cast-iron, over high heat. When pan is hot, pat steaks dry with a paper towel and season generously with salt and pepper. Add steaks to pan and cook about 2 to 3 minutes per side for medium rare. Remove from pan. Cover lightly with foil to keep warm.
Add butter to the pan and cook until butter is a deep golden-brown color. Add the asparagus and onions to the pan and cook, stirring or tossing often, until the vegetables are tender and slightly browned, about 10 minutes. Season to taste with salt and pepper. Transfer to a platter.
Add the red wine vinegar to the pan and allow to reduce by half, about 2 to 3 minutes. Add the cherry preserves and cook until mixture has a sauce consistency, about 2 more minutes. Add the tarragon and the 1 tablespoon coarse-ground black pepper to the sauce. Season to taste with salt and pepper, if necessary.
Arrange steaks on top of asparagus-onion mixture and spoon sauce on top of steaks.