Envy Evangelism?

In Romans, Paul writes, "Inasmuch as I am the apostle to the Gentiles, I make much of my ministry in the hope that I may somehow arouse my own people to envy and save some of them." It's unlikely that the apostle is advocating any structured form of "Envy Evangelism." However, what a blessing it would be if those in our midst, seeing the importance of our salvation in Christ, found themselves wanting to take a closer look at what they’re missing.