Preheat the oven to 425°F.
On a sheet pan, toss the chicken thighs, broccolini, and cherry tomatoes with 2 tbsp olive oil, salt, and pepper, then spread into an even layer.
Roast for 20-25 minutes, until the chicken is cooked through and the vegetables are tender; let the chicken rest briefly, then slice.
While everything roasts, cook the pasta in well-salted water and drain.
Return the pasta to the pot off heat, add the pesto, remaining ½ tbsp olive oil, and a splash of pasta water, and toss until glossy.
Fold in the sliced chicken and roasted vegetables.
Finish with lemon zest, parsley, red pepper flakes, and vegan parmesan if using.