Preheat a grill or grill pan over medium-high. In a large bowl, toss the broccolini with 1 tbsp. oil; season with salt and pepper. Grill, turning occasionally, until charred and tender, about 10 minutes.
Spread the mayonnaise on one side of the bread slices. Divide the cheese, herbs and beefsteak tomato among 4 slices of bread; season. Top with the remaining bread, mayonnaise side down. Brush the outside of the sandwiches with 2 tbsp. oil. Grill until the cheese melts and the bread is grill-marked, 2 to 3 minutes per side.
Chop the broccolini into bite-size pieces. In a large bowl, toss the broccolini with the cherry tomatoes, lemon zest and juice, and the remaining 1 tbsp. oil; season. Serve alongside the grilled cheese.