Place the small saucepan over low heat and add the peanut butter. Warm gently, stirring constantly, until it melts into a smooth, glossy consistency, about 2 minutes. You'll hear a gentle bubbling and see the color deepen slightly.
Add the minced garlic, grated ginger, soy sauce, and lime juice to the saucepan. Whisk everything together until fragrant and smoothly combined, about 1 minute. The mixture should smell savory with hints of citrus and spice.
Pour in the coconut milk gradually, stirring constantly, until the sauce reaches a creamy, pourable consistency. Adjust the heat slightly if needed, but keep it gentle to prevent burning or separation. The sauce will thicken slightly and become silky.
Taste the sauce and stir in honey or maple syrup if you prefer a touch of sweetness. Adjust the acidity with more lime juice or saltiness with additional soy sauce if desired. Keep stirring until well balanced and smooth.
Allow the sauce to simmer gently for another minute, then remove from heat. It should be shiny, smooth, and slightly thickened, with a nutty aroma filling your kitchen.
Pour the finished sauce into a bowl or jar. Let it sit for 5 minutes to meld the flavors, then serve warm or at room temperature as a versatile condiment or dip.