The phrase "a sort of handsome" is correct and usable in written English.
It can be used to describe someone who has an attractive appearance, but with a sense of ambiguity or qualification about their handsomeness.
Example: "He was a sort of handsome, with rugged features that didn't fit the traditional mold."
Alternatives: "kind of attractive" or "somewhat good-looking".
Mirallas, with his sort-of handsome visage and cosmopolitan charms, could front the "moderate" Tories when the in-out referendum on EU membership rolls around, appealing to some of The North and to those who revel in the ballsiness of the well-paid.
You would hardly notice from how carefully they're arranged, but the store carries a handful of additional items: some unfortunate-looking loafers in mealy colors, sharp plaid bow ties made in collaboration with Alexander Olch, robust skin-care products by Aesop, all sorts of handsome satchels by Want Les Essentiels de la Vie.
"But nice, happy guys tend to be like, you know, sort of handsome leading man guys, and I never really nailed that market," he says.
This was the sort of handsome victory to lend credence to Patrick Vieira's claim that Arsenal wanted to win every match from here on in.
On the original launch I thought it was marvellous, exactly the sort of handsome, sophisticated, exhilarating, satisfying grand tourer that Aston Martin should be making and, at the time, probably better than its Italian rivals.
It's actually sort of handsome from the back and sides, but man — the face just seems amazingly gaudy.
I'd submit that it needs some sort of handsome leather sheath, but other than that it looks perfect for just about any outdoor grill.
Especially because Mr. Geithner, the boyishly handsome brainiac, has a sort of otherworldly intensity, as if he's a space alien observing our species at close range and thinking to himself, "Pets, or meat?" (Ha-ha! Joke! I kid because I love. And I meant the part about boyishly handsome).
