Slice sweet potatoes in half and and cut the pointy tips off. Place in a spiralizer and spiralize into noodles.
Heat 1 Tbsp. oil in a large nonstick skillet over medium. Add sweet potato noodles and cook 2 minutes, tossing often. Add 2 to 3 Tbsp. water to create steam in the pan, cover, and cook 5 more minutes, lifting lid occasionally to toss, until tender. Season with 1/4 tsp salt, and transfer to a bowl.
Add 1 Tbsp. oil to the pan and increase heat to medium-high. Add tofu, and season with 1/4 tsp each salt and pepper. Cook 7 to 8 minutes, turning to brown all sides, until golden and crisp. Transfer to bowl with sweet potato noodles, and reduce heat to medium.
Add remaining 1 Tbsp. oil to pan, along with bell pepper and shallots. Cook 3 minutes, until pepper starts to soften. Add red curry paste, lemongrass paste, ginger, and remaining 1/4 tsp each salt and pepper; Cook 2 minutes. Add spinach and soy sauce; cook 1 minute, stirring often, until spinach is wilted. Stir in coconut milk.
Add sweet potato noodles and tofu back to pan. Simmer 4 to 5 minutes, tossing often, until sauce thickens and begins coating noodles. Stir in fresh lime juice and garnish with cilantro.