On a cutting board, using the flat side of a chef's knife, mash the garlic clove to a paste with a pinch of salt; transfer to a large bowl. Add the tomatoes, onion, vinegar and the 3/4 cup of olive oil and season with salt and pepper. Let the mixture stand at room temperature, stirring a few times, for at least 1 hour or up to 2 hours.
Light a grill. Brush the bread with olive oil and grill over high heat until toasted and lightly charred in spots, 1 minute per side. Let cool slightly, then cut into 1/2-inch cubes.
Add the bread and arugula to the tomatoes along with the ricotta salata and toss to combine. Serve right away.