Prepositions – Should ‘On’, ‘Into’, or ‘Onto’ Be Used in This Sentence?

into is not appropriate because we normally only use it when something goes inside something else or is pressed firmly against a surface, possibly changing the shape of the surface. For your sentence, into would be OK if you were to say:

I bite the gingerbread man and his head rolls into my mouth.

We use on when something is in contact with something or makes contact with it.

We use onto only when something makes contact with something.

For most verbs, it is sufficient to use on even when something makes contact with something. In the following examples, we could use onto, but the verb makes it clear that the books and the plate are making contact, so on is sufficient:

Put the books on the table
The plate fell on the floor.

With roll (and move), the situation is different. In the following sentence, the ball could already be on the floor and be rolling along the surface, or it could have rolled off something else and made contact with the floor.

The ball rolled on the floor

If we want to make it clear that the ball was somewhere else, then it rolled and made contact with the floor, we would use onto:

The ball rolled [from the table] onto the floor.

If, on the other hand, we wanted to indicate that the ball were already on the floor, we would use on.

This NGram shows that on is more widely used than onto but onto is becoming increasingly common. If you look at some of the individual instances of each phrase in the past 20 years, you will see a clear distinction in meaning, as described above, between rolled on the floor and rolled onto the floor.

With the head of the cookie, the only one that really works in this situation, where the head rolls and makes contact with the tongue, is:

I bite the gingerbread man and his head rolls onto my tongue.