In a large saucepan over medium, heat the oil until shimmering. Add the onion, sugar and ½ teaspoon each salt and pepper. Cook, stirring occasionally, until the onion is well browned, 12 to 15 minutes. Transfer half to a small bowl; set aside.
Add the thyme to the remaining onion in the pan and cook, stirring, until fragrant, about 30 seconds. Add the rice, tomatoes with juices and broth. Bring to a simmer over medium-high, then cover, reduce to medium and simmer, stirring occasionally, until the rice is tender, 18 to 20 minutes.
Off heat, stir in the parsley, then taste and season with salt and pepper. Garnish with the reserved onion and a drizzle of additional oil.
