Wash the jasmine rice in a colander, moving it around with your hands, until the water runs clear. Drain and set aside.
Heat a the olive oil in a skillet over medium heat. Add the chopped onion, minced garlic, and minced ginger. Sauté until the onion is translucent and fragrant, about 3-4 minutes.
Add the jasmine rice to the skillet and stir to coat the grains with the aromatics. Cook for an additional 2-3 minutes, stirring occasionally, until the rice is lightly toasted.
Transfer the sautéed rice mixture to the rice cooker. Pour in the vegetable broth, then add the soy sauce, mirin and sesame oil. Stir gently to combine.
Place the sliced mushrooms on top of the rice mixture in the rice cooker, distributing them evenly.
Close the rice cooker lid and set it to the "Cook" setting. Let it cook until it switches to the "Keep Warm" mode, usually about 15-20 minutes. Now, leave the rice on warm for 5-10 minutes.
Once the rice is cooked, fluff it gently with a fork to incorporate the mushrooms evenly throughout the rice. Garnish with green onions and sesame seeds.