Combine miso paste, soy sauce, mirin, water, and broth in a medium saucepan. Whisk until the miso is fully dissolved and the mixture is smooth. Bring to a gentle simmer over medium heat, about 2-3 minutes.
2 tablespoons miso paste, 3 tablespoons soy sauce, 2 tablespoons mirin, 1 cup water, 1 cup vegetable or chicken broth
Add sliced carrots to the simmering mixture. Cook for 3-4 minutes until they start to soften and the liquid begins to slightly darken and thicken around the edges.
1 carrot carrot
Stir in the tofu cubes and green beans. Continue simmering for another 5-6 minutes, until the vegetables are tender and the tofu is heated through, ensuring the sauce thickens further and develops a glossy appearance.
1 cup tofu cubes, 1 cup green beans
Heat sesame oil in a small skillet over medium heat. Sauté the mixture gently for 2-3 minutes, stirring continuously until fragrant and slightly caramelized on the edges.
1 tablespoon sesame oil
Pour the aromatic sauce back into the pan if transferred, or serve directly from the saucepan. Cook for an additional 2 minutes to allow flavors to meld and the sauce to thicken to a desired consistency. Watch for a glossy, slightly sticky appearance as a sign of doneness.
Remove from heat and transfer to a serving dish. Garnish with sesame seeds and sliced green onions for color and added flavor. Serve hot.
to taste sesame seeds, to taste green onions