aufgeschnitten
sliced open
Opened or cut into slices with the help of a knife or another sharp object.
Für das Frühstück habe ich frisches Brot aufgeschnitten.
For breakfast, I sliced some fresh bread.

sliced open / boastful
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sliced open
Opened or cut into slices with the help of a knife or another sharp object.
Für das Frühstück habe ich frisches Brot aufgeschnitten.
For breakfast, I sliced some fresh bread.

'Aufgeschnitten' (sliced open/boastful) is the past participle of the verb 'aufschneiden' (to cut open/slice; to boast). Here it is used like a normal adjective and declined before a noun.
Kannst du mir bitte eine aufgeschnittene Zitrone geben?
Could you please give me a sliced lemon?
You can recognize the meaning from the noun being described. If 'aufgeschnitten' (sliced open) refers to food or objects, it means 'cut into slices.' If it refers to a person or their behavior, it means 'boastful.'
Auf dem Tisch stand eine Platte mit aufgeschnittenem Käse.
On the table there was a platter with sliced cheese.
In the literal meaning, the word is almost always used for food. Common combinations are 'aufgeschnittenes Brot' (sliced bread), 'aufgeschnittene Wurst' (sliced sausage/cold cuts), or 'aufgeschnittenes Obst' (sliced fruit).
Für die Party haben wir viele aufgeschnittene Tomaten und Gurken vorbereitet.
For the party, we prepared lots of sliced tomatoes and cucumbers.
The meaning 'prahlerisch' (boastful) or 'angeberisch' (show-offish) belongs to colloquial language. In formal situations or in written language, this use is generally avoided.
Sein aufgeschnittenes Gerede über seine Erfolge nervt alle.
His boastful talk about his successes gets on everyone's nerves.
arrogant
'arrogant' and 'aufgeschnitten' can both describe conceited behavior. 'Arrogant' is more neutral in style and generally means that someone thinks they are better than others. 'Aufgeschnitten' is colloquial and emphasizes more that someone is boasting or talking big. It sounds more casual and often somewhat derogatory. In serious or formal situations, 'arrogant' fits better. In conversations among friends, 'aufgeschnitten' can sound more natural when someone is bragging.

Tom hat wieder aufgeschnitten und erzählt, dass er alles allein geschafft hat.
Tom was showing off again and said that he had done everything by himself.
Die Antwort des Verkäufers war so arrogant, dass der Kunde sofort ging.
The salesperson's answer was so arrogant that the customer left immediately.