Add water to a medium saucepan and bring to a boil over high heat. Stir in rice. Reduce heat to maintain a simmer, cover and cook until the rice is tender and most of the liquid has been absorbed, 35 to 40 minutes. Remove from heat.
Meanwhile, use a vegetable peeler to cut carrot into long, thin ribbons. Combine vinegar, 1 tablespoon tamari (or soy sauce), sesame oil, ginger and sugar in a small saucepan; bring to a simmer. Add the carrot and stir to coat. Remove from heat. Cover and set aside while the rice cooks.
Heat 1 tablespoon canola (or grapeseed) oil in a large nonstick skillet over medium-high heat. Add mushrooms and cook, stirring often, until tender, about 5 minutes. Add spinach and the remaining 1 tablespoon tamari (or soy sauce) and cook until wilted, about 30 seconds. Transfer to a bowl.
Pat shrimp dry and sprinkle with gochugaru. Add the remaining 1 tablespoon oil to the pan. Add the shrimp and cook, stirring occasionally, until lightly browned and cooked through, 3 to 4 minutes.
Strain the carrot-soaking liquid into the rice. To serve, top the rice with the vegetables and shrimp and garnish with cilantro, if desired.
