The `Broadcast`/`ResendWalletTransactions` interface is strange:

- it's the node saying to the wallet "Try to submit your unconfirmed transactions to the mempool again"
- it's called in one place by the node, in `SendMessages()` here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/net_processing.cpp#L3515. `SendMessages()` is called on the message handling thread on a loop.
- the actual scheduling of when the wallet sends messages is handled in the `ResendWalletTransactions()` function itself, using the `nNextResend` and `nLastResend` wallet globals (which could as easily be static variables in `ResendWalletTransactions()`).

Therefore the only use of `Broadcast()` is to periodically prod the wallet. The wallet itself decides whether it's time to resend transactions. This could be done by scheduling regular calls to `ResendWalletTransactions()`, in the same way that we schedule regular wallet flushes here: https://github.com/bitcoin/bitcoin/blob/c033c4b5cef89a654e4d9d5c5f9bd823871b068b/src/wallet/init.cpp#L215.

A couple of minor implementation details:

- the call to `Broadcast()` in `SendMessages()` is protected by an if statement `if (!fReindex && !fImporting && !IsInitialBlockDownload()) {`. Those tests could be moved into `ResendWalletTransactions()` (through the `Chain` interface).
- The `Broadcast` notification passes in the `nTimeBestReceived` time of the best block. That could be fetched by `ResendWalletTransactions()` through the `Chain` interface.
};
static CMainSignals g_signals;
static std::unordered_map<CTxMemPool*, boost::signals2::scoped_connection> g_connNotifyEntryRemoved;
void CMainSignals::RegisterBackgroundSignalScheduler(CScheduler& scheduler) {
    assert(!m_internals);
    m_internals.reset(new MainSignalsInstance(&scheduler));
}
void CMainSignals::UnregisterBackgroundSignalScheduler() {
    m_internals.reset(nullptr);
}
void CMainSignals::FlushBackgroundCallbacks() {
    if (m_internals) {
        m_internals->m_schedulerClient.EmptyQueue();
    }
}
size_t CMainSignals::CallbacksPending() {
    if (!m_internals) return 0;
    return m_internals->m_schedulerClient.CallbacksPending();
}
void CMainSignals::RegisterWithMempoolSignals(CTxMemPool& pool) {
    g_connNotifyEntryRemoved.emplace(std::piecewise_construct,
        std::forward_as_tuple(&pool),
        std::forward_as_tuple(pool.NotifyEntryRemoved.connect(std::bind(&CMainSignals::MempoolEntryRemoved, this, std::placeholders::_1, std::placeholders::_2)))
    );
}
void CMainSignals::UnregisterWithMempoolSignals(CTxMemPool& pool) {