Combine broth and 1 cup water in a saucepan; bring to a simmer over medium heat. Reduce heat and keep warm.
Heat 1 Tbsp. of the oil and butter in a large skillet or wide-bottomed pot over medium heat. Add mushrooms; cook 5 minutes, until golden-brown. Season with 1/4 tsp. of the salt and transfer to a bowl. Add remaining 1 Tbsp. oil to pan. Add shallots and garlic; cook 1 to 2 minutes, until softened and aromatic. Add rice and remaining 1/4 tsp. salt; stir to coat all the grains, 1 minute. Add 1 ladle of broth (½ cup to ¾ cup), stir, and leave it alone until broth is nearly absorbed, 2 to 3 minutes.
Stir, add another ladle of broth, and stir again. Cook undisturbed until the broth is absorbed, 3 minutes. Repeat until all broth has been absorbed and rice is tender, 15 to 20 minutes of total cook time for the rice. Turn off heat.
Stir in miso paste and soy sauce. Add mushrooms back to pan; toss to combine. Ladle risotto into bowls and garnish with green onions and additional toppers (poached eggs, sesame seeds, greens, etc.), if desired.