First of all, last week, the lesson was about the participio presente (present participle). Guarda caso (it just so happens) that this week, there is a perfect example of the present participle in the segment of Liberi tutti. It's not quite an expression, but for the purposes of this lesson, we think it can pass.
Sedicente
The breakfast conversation is partially about a guy who calls himself a prince. Riccardo uses the adjective sedicente. We bring it up because it is a perfect example of the present participle used as an adjective. Remember the rule? We can replace it with che and the conjugated verb. In this case, the caption is:
C'è questo sedicente Ciro, Principe di Filicudi, che rivendica tutto il Nido.
There is this self-styled Ciro, Prince of Filicudi, who is laying claim to the entire Nest.
Captions 58-59, Liberi tutti EP2 Ci vivresti on un posto così? - Part 1
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We can translate it with "self-styled" or "so-called," depending on the context.
We just thought it was kind of fun to see this example after having talked about it so recently. We will be adding it to last week's lesson as an update.
Palle
There's another expression from the same video. This one is rather vulgar, but it's used often enough that it's good to understand what it means, even if you choose not to use it (a good choice, especially in polite company).
Di solito a quest'ora vi girano le palle almeno fino alle nove e oggi, stamattina, Fedez. E proprio perché ci girano le palle, parlavamo di Fedez.
Usually at this time your balls are spinning [you're pissed off] until at least nine o'clock and today, this morning, Fedez. And precisely because our balls are spinning, we were talking about Fedez.
Captions 39-41, Liberi tutti EP2 Ci vivresti on un posto così? - Part 1
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Girare means to turn or to spin. This expression is typically used when you are generally in a bad mood because of something that has happened.
It can get more personal with the verb rompere (to break). When someone made you mad and you can't stand it any longer, you can talk about the balls breaking. It can also be translated with "to bother."
Invece di fermare gli spacciatori, vengono a rompere le palle a noi.
Instead of arresting the drug dealers, they come and break our balls.
Caption 4, Provaci ancora prof! S1E1 - Il regalo di Babbo Natale - Part 14
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A ball-breaker is un rompipalle. The more polite version is rompiscatole (box-breaker). It can refer to someone who keeps at you, and doesn't let you alone.
As you may have noticed in other videos, Italians use images of male private parts in a whole range of expressions.
For more about using palle, especially in arguments, see this lesson.
Here, we are talking about balls. Usually, there are two, but when talking about something being boring or annoying, sometimes just one is used.
Era una palla (it was a real bore).
Provolone
In this week's episode of Sposami, Melody describes Manrico as un provolone. It's kind of a cute double-entendre. You might have heard of the cheese provola or provolone.
Certe volte è tenero, è delicato. Poi, all'improvviso, si trasforma in un, in un provolone che pensa a una cosa sola.
Certain times he is tender, he is gentle. Then, all of a sudden, he is transformed into a, into a playboy who thinks of one thing only.
Captions 54-56, Sposami EP 6 - Part 7
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But nested in the word provola or provolone is the verb provare. It means "to try," but it also means, especially as part of the compound verb provarci, to hit on someone, to flirt heavily. Check out our lesson about provarci. Un provolone hits on any and all women (typically).