Set the oven to 200°C (390°F). Slice tomatoes, potatoes, and carrots into uniform pieces. Toss with olive oil, minced garlic, salt, and pepper. Spread on a baking sheet.

Place the baking sheet in the oven and roast for 12-15 minutes until vegetables are tender and slightly caramelized.

Meanwhile, bring a pot of water to a gentle simmer. Crack eggs into individual cups, then slide into simmering water. Cook for 3-4 minutes until whites are set but yolks remain runny.

Transfer roasted vegetables to plates, sprinkle with chopped herbs, and top each with a poached egg. Season with additional salt and pepper if desired.