To make the vinaigrette, stir everything together in a small bowl. If making ahead, cover and refrigerate.

To prepare the salad, preheat the oven to 350°F.

Spread the barley in a single layer on a baking sheet and toast until golden brown, about 12 minutes. Remove from the oven.

Bring a saucepan of salted water (add about 1 tablespoon salt for every quart of water) to a boil over high heat. Add the toasted barley and cook until just al dente, about 12 minutes. Drain, transfer to a large bowl, and set aside to cool to room temperature.

Add the tomatoes, shallots, and herbs. Cover and set aside.

If you’re not using the cinder block pit to cook, heat a cast-iron griddle or skillet over high heat until it’s smoking hot. Rinse the squid under cool water and remove the quills, if there are any. Pat the squid dry with paper towels and season them all over with salt and pepper. Cook the squid on the griddle or in the skillet until tender and browned in places, about 5 minutes, turning them occasionally. Transfer the squid to a plate and set aside to cool slightly.

Drizzle the salad with the vinaigrette and toss gently to combine. Add the squid and toss again. Serve while the squid are still slightly warm or at room temperature, with aioli on the side.