Preheat the oven to 375°F (190°C).
Wash the squash, trim the stem end, then cut each squash in half 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 a few minutes after removing from oven.
Alternatively, place cut-side down in a microwave-safe dish with about 1 inch of water and microwave on high until tender, about 10–12 minutes.
While the squash cooks, make the peanut sauce: combine creamy peanut butter, 1/4 cup warm water (reserve more to thin as needed), minced ginger, minced garlic, fresh lime juice, and Tamari or soy sauce in a blender or food processor and puree until smooth; add additional warm water 1 tablespoon at a time if needed for a pourable consistency.
Using a fork, scrape the cooked squash flesh from each shell into a bowl, keeping the shells intact for serving.
Pour the peanut sauce over the warm squash strands and toss until evenly coated; taste and adjust salt if desired.
Spoon the sauced spaghetti squash back into the reserved shells and divide between serving plates.
Top with roasted salted peanuts, fresh cilantro leaves, and lime wedges; optionally add warmed cooked tofu or chicken to individual servings.
Serve immediately while warm; if not serving right away, warm the peanut sauce before mixing with squash so the dish is hot when served.