These cookies are fun to make and especially fun to eat.
As the OP suggests, this is a Conjunction Reduction of
- These cookies are fun to make and these cookies are especially fun to eat.
Let's just take one of these, OK? It's the same structure in both conjoined clauses.
- These cookies are fun to make.
The OP also notes that these cookies is the Direct Object of the infinitive to make
and normally what one expects to be moved or missing from an infinitive is its Subject, not its DO.
And indeed the subject of each infinitive is missing, but that's normal for indefinites.
The real question is how the infinitive make wound up shorn of both its Su and its DO,
and how the DO of make wound up as the Su of be fun.
And the answer is a minor governed cyclic rule called Tough-Movement.
A "governed" rule is one that requires the presence of some particular (kind of) predicate. We say that the rule is governed by the predicate; in this case, Tough-Movement is governed by be fun.
A governed rule is called "minor" if it only applies to a relatively small number of predicates.
In this case, fun is one of a relative handful of predicates, all taking infinitive complements, e.g: tough, easy, difficult, hard, a bitch, a breeze, a piece of cake, fun, cool, nice.
What the rule does is sort of like A-Raising,
in which the Su of an infinitive winds up as upstairs Su, e.g:
- It seems to be a long way to Tipperary.
- There is likely to be a unicorn in the garden.
- The shit appears to have hit the fan.
Here the boldfaced idiomatic or dummy subjects of seem, likely, and appear
(all of which govern A-Raising) are unambiguously licensed by (or "originated in", as one says when one uses the "movement/raising" metaphor theme) the infinitive complement clauses:
(Extraposition and There-Insertion have generated the It and There dummies,
and the idiom chunk subject in the last sentence clearly goes with hit the fan.)
But this is A-Raising, however, a major governed rule, very frequent with many predicates.
Tough-Movement, by comparison, works exactly the same way as A-Raising, with two differences:
- Tough-Movement raises the Object of the infinitive clause, and not its Subject
- A small set of predicates governs Tough-Movement, and a large set governs A-Raising
(these sets are disjoint, btw; no predicate governs both.)