Heat the vegetable oil in a medium saucepan over medium heat until shimmering, 1–2 minutes.
Add the onion and garlic and cook, stirring, until translucent and softened, 3–4 minutes.
Stir in the mango, habanero chiles, apple cider vinegar, water, granulated sugar, and kosher salt; bring to a simmer.
Simmer gently, stirring occasionally, until the mango is very soft and the liquid has reduced slightly, 12–15 minutes.
Blend the hot mixture carefully with an immersion blender (or in a vented countertop blender) until perfectly smooth and velvety, 1–2 minutes.
Return the sauce to the saucepan over low heat and simmer, stirring, until it lightly coats the back of a spoon, 3–5 minutes. Stir in the lime juice.
Remove from the heat and whisk in the unsalted butter until glossy and emulsified, 30–60 seconds. Let stand 5 minutes before tossing with hot, crispy wings or cooling for storage.