Rinse rice well under cold running water; drain. Combine rice and broth in a saucepan. Cover and bring to a boil over medium heat. Reduce heat to medium-low and simmer until rice is tender but still has a little bite, about 7 min. Meanwhile, in a small saucepan, combine rice vinegar and sugar; bring to a boil. Remove rice from heat; stir in vinegar mixture. Cover pan with a clean towel, replace lid and let sit for 5 min.
Heat oil in a skillet over medium-high heat. Add mushrooms and cook, stirring until tender, about 2 min. Add green onions and garlic; cook 1 min. Stir in soy sauce and transfer to a bowl. Stir in pickled ginger; cool.
In a small skillet over medium heat, toast sesame seeds until golden, about 2 min., stirring occasionally. Transfer to a plate. Divide warm rice into 8 portions. Using wet hands to prevent sticking, gently mould one portion into a ball. Make a dent in centre and place 1/8 of the filling mixture into the dent. Mould rice around filling. Roll in sesame seeds. Repeat to make remaining balls. Cover until ready to serve.