Matthew is often called the “Jewish Gospel” because of all the fulfillment formulas. However, I think that is a rather static view of the book. The book ends with the Great Commission, which is to extend the gospel to all the nations. If Matthew is only a “Jewish Gospel” then the great commission must be a bit of a misfit.
However, I think that Matthew has as it’s purpose to present Christ for the nations. Consider that the Genealogy includes gentiles and is wrapped around the Babylonian exile, that the Magi from the east (Babylon?) somehow invade the Christmas story in Matthew 2. The disciples are called, instructed, trained, rejected and finally sent into the world. So I think it is fair to say that Matthew has two movements.
First, it is about Jesus fulfilling the role of Messiah
Second, it is about being the Messiah for the nations.
My tentative sermon series title then is: Matthew – Fulfill and Fill Full