Whisk coconut milk, peanut butter, soy sauce, brown sugar, lime juice, Sriracha sauce, and ground chili pepper together in a bowl until a smooth sauce forms.

Heat oil in a large skillet over medium-high heat. Add carrots and bell pepper; sauté until just tender, 1 to 2 minutes. Add tofu and sauté until lightly browned, about 4 minutes per side. Add garlic and ginger; cook and stir until fragrant, about 30 seconds.

Pour sauce into the skillet and stir to coat tofu and vegetables. Cook until flavors combine, about 5 minutes. Reduce the heat to low, then stir in spinach, 1 cup at a time, until wilted. Serve over brown rice.