Cut the fennel bulb in half lengthwise and then into one-centimeter-thick wedges, leaving a piece of the tough core attached to each wedge. This core holds the layers together so the wedges don't fall apart in the grill pan.
Rub the wedges with a tablespoon of olive oil and salt. Heat a grill pan until almost smoking and grill the fennel for three to four minutes per side until it has dark grill marks and is almost charred at the thin edges. Fennel contains a lot of water and little starch; only high heat evaporates this water quickly enough to brown before the wedge turns soggy. Let the wedges cool slightly.
Rinse the white beans under cold water until the foam disappears and drain them well. Mix them in a bowl with the grated garlic, two tablespoons of olive oil, a generous squeeze of lemon juice, some lemon zest, salt, and black pepper. Mash a small handful of beans against the side of the bowl; this makes the dressing creamy without needing to add anything else.
Toast the almonds in a dry frying pan until fragrant and roughly chop them. Halve the cherry tomatoes.
Arrange the arugula on a plate, spoon the beans over it, and tuck the grilled fennel and tomatoes in between. Shave the pecorino over it in flakes and finish with the almonds, parsley, and mint.