Learn German: Wir essen immer exakt dasselbe Frühstück. - We always eat exactly the same breakfast.

Because it has to match the gender and case of the noun it refers to, which is das Frühstück (the breakfast). Since the breakfast is the direct object of the verb essen (to eat), it needs to be in the accusative case. For a neuter noun in the accusative case, the correct form is dasselbe.

If they are eating dasselbe Frühstück, does that mean they are sharing one single plate of food?

Technically, yes! In strict German grammar, dasselbe means the exact same physical item, while das gleiche means two different items of the same type (like two separate bowls of oatmeal). So if they are not sharing a plate, they are technically eating das gleiche Frühstück. However, in everyday spoken German, native speakers frequently mix these up and use dasselbe for both, just like in English.

Why is dasselbe written as one word, whereas das gleiche is written as two?

The words derselbe, dieselbe, and dasselbe are demonstrative pronouns that are always written together as a single word. They are a fusion of the definite article (das) and the adjective selbe. On the other hand, gleich is treated as a normal adjective, so it stays separated from its article, like in das gleiche.

Could I use genau instead of in this sentence?