Broussard here starts off badly by attacking a strawman. The idea that the disciples stole Jesus' body and made up the resurrection story is not something that anyone necessarily needs to take seriously. It is more likely as an explanation of an empty tomb than an actual resurrection would be—people involved in founding religious sects often do engage in frauds, just see Joseph Smith for an example—but we don't have any particular reason to believe that there was an empty tomb at all, even assuming Jesus did exist as a historical person. If there were strong evidence for an empty tomb, then we would have to consider the question of how that happened.
But even so, Broussard's argument is remarkably weak.
A recent article by Neil Godfrey on Vridar is titled “How Many Bible Verses Does It Take to Prove Jesus Existed?”. Godfrey points out the extent to which theological or apologetic responses to Jesus-mythicist arguments simply pull out a proof-text, such as Gal 1:19 “James the Lord’s brother”.
Broussard's first proof-text is 1 Cor 15, which he seems to think shows that early Christians had “nothing to gain and everything to lose” by lying about the resurrection. But there is a fundamental flaw here in that Paul on his own testimony has not seen any empty tomb and saw the ‘resurrected’ Jesus only in a vision; assuming he's not lying about that, then he's also on the outside of any hypothetical conspiracy.
Can it be argued that the original hypothetical conspirators would have no motivation to do it? On the contrary, people do things for any number of irrational reasons. Again, the Mormons are an instructive example: a bunch of people swore affidavits about having seen the golden plates; why would they lie about that?
Broussard's second proof-text is Josephus' comments on the testimony of women. Carrier has a chapter on this in Not The Impossible Faith which covers the subject in detail; but Broussard seems to think he can refute this just by quoting Josephus again with no serious effort to address any other part of the argument. But what of the fact that Paul—who mentions no empty tomb story—reveals in his letters that women had a significant role in early Christianity? It is quite possible (on the conventional assumed datings, almost certain) that the earlier Gospels pre-date the attempts of the Pastoral author to restrict the role of women.
Moreover, Josephus was a Pharisee—and Rabbinic Judaism descends from the Pharisees—whereas the Gospels depict the Pharisees as opponents. So the appeal to Pharisaic law when analyzing the Gospels is fundamentally misguided.