Heat the oven to 425°F and line a rimmed sheet pan with parchment.
Coat the chicken with 1/4 cup pesto and salt, toss the tomato slices with olive oil and arrange both on the pan without overlapping.
Roast the tomatoes for 12 minutes and the chicken for 16 to 20 minutes, removing each when ready and verifying the chicken reaches 165°F.
Rest and thinly slice the chicken, then lower the oven to 375°F.
Slice the connected rolls horizontally and layer the bottom slab with remaining pesto, mozzarella, sliced chicken and roasted tomato.
Replace the roll tops, brush with melted butter, cover with foil and bake for 8 minutes; uncover and bake for 4 minutes more.
Rest for 5 minutes and separate the 12 sliders along the seams.