The "Uʻi" at the front of "Uʻi ka mahiʻai" equates to "[to be] handsome," making "Uʻi ka mahiʻai" a complete statement, "The farmer is handsome," rather than just saying "the handsome farmer." I think the handsome farmer would be: "ka mahiʻai uʻi," where "uʻi" is a modifier and follows the thing it's describing.