Heat a large saucepan over medium-high heat. Saute onion, garlic, and herbes de Provence. Add some vegetable broth if the mixture is too dry. Add mushrooms and leeks; cook until heated through, 3 to 4 minutes.
Pour remaining vegetable broth and rice into the mushroom mixture. Add soy milk and vinegar. Let simmer until liquid is absorbed, stirring occasionally, 15 to 20 minutes.
Stir peas, lemon juice, and nutritional yeast into the rice mixture. Cook until peas are warmed through, about 3 minutes. Turn off heat; season with salt and pepper.