Not sure what this is called, but I have seen the following phrases with and without hyphens:
The doctor performed a well-documented procedure.
Or:
He took an often-used road to the farm.
What are those 'contraptions' called, and should hyphens be used or do they go separate (well documented and often used)?
Both uses you've quoted should use a hyphen. You may see the same phrase without, as in "the procedure was well documented", where the hyphen isn't necessary. In both the examples you show, there's not much room for confusion without the hyphen, but in similar constructions there may be. Finally there is a difference between a hyphen and a dash (of which there are two main types and several uses). Here it is a hyphen that is required—which is the easy one to type in. For more detail see "dash" on Wikipedia.
These are regarded as a kind of compound. See the quotations in Sven Yargs' answer to Should there be a hyphen in expressions such as "currently-available X"?
Many style guides recommend using a hyphen between an adverb and adjective that modify a following noun, except for when the adverb is very or ends in -ly. As well and often do not end in -ly, is is permissible and possibly advisable to use a hyphen.
When there is no following noun (as in "The procedure is well documented" or "The road was often used"), it may be best not to include a hyphen. Another question asks about the use of hyphens in that context: "You should be well-organised" or "You should be well organised"?
The question being: since “well” is an adverb, not an adjective, we do not hyphenate “well documented”. The doctor performed a well documented procedure. The adverb “well” cannot modify the noun “procedure” so there can be no confusion.
Similar: an awfully big adventure and not an awfully-big adventure.
When “well” is replace by something not clearly an adverb, then probably you should hypenate: the three-hour tests
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A comment by @Chemomechanics suggests I am wrong. And I have come to the conclusion that I am, indeed, wrong.
Fowlers' Modern English Usage (3rd edition) even has an entry on well and well-. They note “widespread uncertainty” on well followed by a participle. But they advocate a hyphen for attributive uses (a well-documented procedure) but not for predicative uses (The procedure is well documented).
personal
As a mathematician I often see “well ordered set” and similar phrases in mathematical literature. My original tendency was to write it with hyphen (well-ordered set) and found that was not the standard, so I tried to wean myself from that practice and write without (well ordered set).
But today, prompted by Chemomechanics’ comment, I did some searches of mathematical literature. To my surprise, nowadays “well-ordered set” far outnumbers “well ordered set”. I guess I can therefore lapse back to my original tendency.
Of course, by the rule quoted in Chemomechanics’ comment, I should still write the -ly cases without hyphen: "partially ordered set", "totally ordered set", "linearly ordered set".
A hyphen is not required, just as it is not required with any other adverb in that construction. A good test is if you wouldn't use a hyphen with a word ending in "ly", then don't use it with "often" or "well" or any other non "ly" adverb.
He took an often used road to the farm. (Not: He took an often-used road to the farm.)
He took a well used road to the farm. (Not: He took a well-used road to the farm.)
He took a universally used road to the farm. (Not: He took a universally-used road to the farm.)
An example of correctly using "well" with a hyphen is: The well-located technology was positioned at the oil rig. "Well" in this case is an adjective (or a noun acting as an adjective) because it refers to a physical well: an oil well. "If you say the technology is well located," still referring to the same oil well, you would NOT use a hyphen.
