Prepare the grill (medium-high heat) or heat an indoor grill-pan on high. Whisk the oil, mustard, garlic, lemon juice, and thyme in a small bowl to blend. Season with salt and pepper, to taste.
Pour the marinade over the fish (or marinate in a zip-lock bag) and refrigerate for 10-15 minutes. (any longer and the lemon will start to cook the fish).
Meanwhile, in a medium bowl, add the tomatoes, oil, basil, and vinegar. Sprinkle with sea salt and pepper to taste. Stir together and let sit for a few minutes so the tomatoes soften a little.
Take the fish out of the fridge and wipe some of the marinade off with a paper towel. Grill the fish until just cooked through, about 3-4 minutes per side (depending on thickness of steaks).
In a medium sauté pan on medium-high heat, add oil and butter and melt until foaming. Add the ramps and sauté, turning around the pan until the bulbs are slightly soft and gently brown in spots and the greens are wilted. Season with salt and pepper.
To serve: Transfer the fish to plates and spoon some tomatoes (and the juices) over the fish. Garnish with the sautéed ramps and serve.