Start bringing a large pot of salted water to a boil.
Meanwhile, heat 3 tablespoons oil on medium-low in a large sauté pan.
Add garlic and allow to cook 10 minutes, until oil is fragrant but garlic has not browned. Remove garlic (save for another use).
When water boils, stir in pasta.
Add tomatoes to oil in sauté pan, increase heat to medium-¬high and, when tomatoes start to shrivel and collapse, reduce heat to low and cook until softened but not shapeless, about 5 minutes. Stir a couple of times. Reserve ½ cup of pasta water.
Drain pasta and add to tomatoes, folding both together. Add some pasta water if needed for moistening. Fold in arugula and remaining oil. When arugula has just wilted, season dish with salt and pepper. Serve with a dusting of cheese. Or serve in about 30 minutes, just warm.