Combine the Dijon, juice of 1 lemon, thyme, garlic powder, 1/2 teaspoon pepper and 2 tablespoons of the vegetable oil in a small bowl; whisk until combined and homogenous.
Remove 2 tablespoons of the marinade and rub all over the steak for 1 minute. Let sit for 10 minutes at room temperature.
Meanwhile, whisk the juice of the remaining 1/2 lemon and the honey into the remaining marinade until the honey is blended. Season with salt. While whisking slowly, add the olive oil. Whisk constantly for 2 minutes; set aside to dress the salad later.
Heat a large ovenproof saute pan over high heat for 2 minutes 30 seconds. Season the steak all over with 1 teaspoon salt.
Add the remaining 2 tablespoons vegetable oil to the hot pan, then add the steak. Cook until crusty and browned, about 1 minute on each of the 4 long sides of the steak.
Place in the oven for 3 minutes. Remove the steak from the pan and let rest for 2 minutes before serving.
Meanwhile, toss the mixed greens with the dressing. Slice the steak and serve alongside the salad.