Brush a grill or grill pan with 1 tbsp. oil; heat over mediumhigh. Rub the steak with the paprika and season generously with salt and pepper. Grill the steak until browned, about 3 minutes per side for medium-rare. Transfer to a cutting board and let rest.
Meanwhile, in a medium skillet, heat 2 tbsp. oil over medium. Cook the tomatoes, swirling the pan until they burst, 4 to 5 minutes. Using a wooden spoon, gently press the tomatoes to release some of their juices. Off heat, stir in the sugar; season. Using a slotted spoon, transfer the tomatoes to a medium bowl.
Whisk the vinegar into the juices in the skillet, then whisk in the remaining 2 tbsp. oil; season the dressing. Add the arugula and fennel to the tomatoes and toss with 1 tbsp. dressing; season.
Slice the steak and divide among 4 plates. Drizzle the steak with the remaining dressing; season. Top with the chips, then mound the salad on top. Garnish with the Parmesan.