In a large glass baking dish, whisk the red wine, mustard, brown sugar, garlic, shallots, parsley, thyme, 1 tablespoon of salt and 1 teaspoon of pepper. Add the steak and turn to coat. Let stand at room temperature for 2 hours or refrigerate for up to 8 hours.
Meanwhile, in a medium bowl, whisk the cider vinegar and honey. Add the tomatoes and onion and toss. Let stand for 1 hour.
Light a grill. Coat the asparagus and corn with olive oil and season with salt and pepper. Grill over moderately high heat, turning occasionally, until tender and browned in spots, about 3 minutes for the asparagus and 6 minutes for the corn. Transfer to a work surface; when cool enough to handle, cut the asparagus into pieces and cut the corn from the cobs. Add the asparagus, corn and basil to the tomatoes and toss.
Remove the steak from the marinade and pat dry with paper towels; season lightly with salt and pepper. Grill the steak, turning once, until medium-rare, about 10 minutes total. Transfer the steak to a work surface and let rest for 10 minutes.
Meanwhile, in a skillet, melt the butter. Add the morels and cook over moderately high heat until browned, about 3 minutes. Season with salt and pepper.
Thinly slice the steak against the grain and transfer to plates. Season the tomato salad with salt and pepper and spoon alongside the steak. Top the steak with the morels and serve.