The one-name connection note
Open a cold contact by asking for a single piece of local knowledge that has a name as its answer, with no job attached.
When to send: As the note on a connection request, within a day or two of actually reading something the person wrote, and before you have applied anywhere. Send it to someone who hires in your field in the city you are moving to.
[FIRST NAME], your post on [EXACT CLAIM] is why I'm writing. I'm a [ROLE] moving to [CITY] in [MONTH]. Which [INDUSTRY] employer here have you seen open a visa case for a non-EU hire? A name is enough, no vacancy talk.
300 character connection note. This line is not part of it. Naming the exact claim in their post proves you read it rather than mail-merged them, and the question can be answered with one company name from memory, which is the cheapest thing a stranger can give you. As written the note runs 218 characters and about 243 with ordinary replacements, so keep long company names short.