Preheat the oven to 375°F (190°C).
Wash the spaghetti squash, cut off the stem, then halve lengthwise and scoop out the seeds.
Brush the cut sides with olive oil and season with 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.
Place squash halves cut-side down on a baking sheet and bake until fork-tender, about 30–40 minutes. Let cool for a few minutes until safe to handle.
While the squash cooks, make the peanut sauce: combine creamy peanut butter, 1/4 cup warm water (add more as needed), minced ginger, minced garlic, lime juice, and Tamari in a blender or food processor and blend until smooth.
Using a fork, scrape the spaghetti-like strands from the cooked squash into a medium bowl, leaving the shells intact for serving.
Pour the peanut sauce over the warm squash strands and toss to combine; taste and adjust salt if needed.
Divide the sauced squash between the empty shells, then top each with roasted peanuts and fresh cilantro and serve with lime wedges.
Optional: top individual servings with warmed cooked cubed tofu or chicken before serving.
If not serving immediately, warm the peanut sauce separately before tossing with squash to keep the dish piping hot.