Now sometimes it is said that knowledge is primarily knowledge-that, i.e. some elementary epistemic operator is a propositional operator/"attitude report". Or at least there is an invoked distinction between descriptive knowledge and knowledge-by-acquaintance, where the formerly is roughly propositional (or at least perhaps covers the obtaining of states of affairs).
At any rate, in English, I think I almost always see the concept of beauty applied as a predicate on objects, as in, "This painting is beautiful," and I can't recall a clear instance of this application being a propositional attitude report, as in, "It is beautiful that this painting exists/has the content it does" (or whatever). Just the same, the grammatical construction "beautiful that..." is permissible, and we do more often say comparable things like, "It's wonderful that..." or, "It's splendid that..."
Now, as far as my judgment of Kant goes, he uses cognition (or rather its German cognate) the way we (if "we" are "analytic philosophers") tend to use proposition. For example, we say that propositions are the primary bearers of truth-values, Kant says that truth is "the accordance of a cognition with its object." When Kant speaks of conceptions and intuitions as objective cognitions, he seems to contrast the apprehensive mode of intuition ("bare sensation") from a sentential mode (an intuition as an apprehension not of individual concept-applications, but of a sentential array of these applications).
And so he has an intricately intellectualized theory of aesthetics, one grounded in the "faculty of judgment," where for him, judgments are broadly equivalent to, or a possible subset of, cognitions. Not that he commits us to a doctrine of aesthetic cognition straightforwarldy, only that the source of cognition, in the faculty of judgment, also has this weird side-output, aesthetic representation, which is at least para-cognitive (so to say). As we (again, "analytic philosophers") are often tempted to emphasize knowledge-that over "smaller" term knowledge, is Kant implicitly committed to representing beauty (and sublimity) in terms of "beautiful-that" more than as a predicate on object terms? At the very least, the SEP article on Kant's aesthetics says:
More strongly, judgments of beauty are not to be understood as predicating the concept beauty of their objects: as he puts it later, “beauty is not a concept of the object” (§38, 290).
EDIT: Insofar as Kant holds that, "I think," accompanies all our representations(?), he does have a generic propositional (or cognitive, or whatever) operator that would perforce range over our aesthetic judgments. This doesn't "prove my point" (since, "I think that it is beautiful that..." is not inferrable from the bare apperception operation, of course), but I do wonder if a "beautiful-that" moment could be construed as a (non-factive) second-order propositional attitude report, applying to, "I imagine (that...)," here, then. Admittedly, "I think that I imagine that it is beautiful that..." doesn't sound at all like what Kant was trying to get across, though.