In a large, deep skillet over medium-high heat, melt the butter. Add the chopped mushrooms and diced onion. Cook, stirring often, for about 2 minutes until softened and fragrant.
Stir in the garlic and jasmine rice. Cook for another minute, letting the rice lightly toast and absorb the flavors.
Pour in the chicken-style broth, tamari, sesame oil, and black pepper. Stir to combine.
Bring to a boil, then reduce heat to low. Cover and let simmer for about 20 minutes, until the liquid is absorbed and the rice is tender.
Remove from heat. Use a fork to gently fluff the rice. Sprinkle with sliced scallions and serve hot.