Press the tofu for at least 30 minutes to remove excess moisture. While waiting, whisk together soy sauce, sesame oil, rice vinegar, garlic, and ginger in a bowl.
Cut the tofu into cubes and marinate in half of the sauce mixture for 15-20 minutes.
Clean the mushrooms and slice larger ones into thick pieces. Toss with olive oil and season with salt and pepper.
Preheat your grill or grill pan to medium-high heat.
Grill the marinated tofu for 3-4 minutes per side until golden brown with nice grill marks.
Grill the mushrooms for 4-5 minutes, turning occasionally, until they're tender and slightly charred.
In a large bowl, arrange the salad greens and sliced bell peppers.
Top with the grilled mushrooms and tofu, drizzle with the remaining sauce, and sprinkle with sesame seeds if desired.