Whisk the 2 tbsp extra-virgin olive oil, lemon juice, 1 tbsp honey, Dijon, salt, and pepper in a small bowl until glossy and emulsified. Set aside.
Pat the halloumi dry and cut it into 1 cm / 1/2-inch slices. Halve the figs lengthwise. Brush the halloumi and the cut sides of the figs with the 1 tbsp olive oil.
Heat a 26 cm / 10-inch cast-iron grill pan over medium-high heat for 3 minutes. Grill the halloumi in two batches, in a single layer with space between the slices, for 2 minutes per side, until dark grill marks form and the edges turn golden. Wait until each slice lifts easily before flipping, because flipping early tears the cheese and leaves it stuck to the pan.
After the second batch, place the figs cut side down in the pan and grill for 2 minutes, until they soften and the edges caramelize. Move the figs and halloumi to a plate.
Toss the arugula and mint with half the dressing in a large bowl, then spread it on a platter. Top with the warm halloumi and figs, spoon over the remaining dressing, scatter the pistachios, and drizzle with the remaining 1 tbsp honey. Serve right away, within 10 minutes of grilling.