Learn Spanish (Latin America): Se me salpicó el aceite enfrente de la estufa. - I accidentally splashed the oil in front of the stove.

In this accidental construction, you are not the grammatical subject. The subject is the oil (el aceite). Because the oil is a singular noun, the verb takes the third-person singular form salpicó. The pronoun me acts as an indirect object to show who was affected by the accident.

How does the accidental se construction actually break down in this sentence?

It uses se (to show an unexpected or involuntary event) + an indirect object pronoun (me, showing it happened to you) + the verb conjugated to the item involved. Literally, it translates to "The oil splashed itself to me," which is how Spanish takes the blame off you for the accident!

Could I just say "Salpiqué el aceite" instead?

You could, but it changes the meaning. Salpiqué el aceite sounds like you splashed the oil intentionally! Using the se me structure is crucial here to communicate that it was a clumsy mistake or completely involuntary.

I originally learned that estufa means "space heater." Does it mean something different here?

Yes, in most of Latin America, estufa is the standard, everyday word for a kitchen stove. In Spain, you would more likely hear cocina or fogones for a stove, while estufa is strictly reserved for space heaters.