[g_b]

Easier to read version:

    let logNow = (importance, message) => log(new Date(), importance, message);
    let debugNow = message => logNow("DEBUG", message);

And with this implementation, current IDEs provide a more informative auto-complete.

[zodiakzz]

Wrong. Your implementation loses all parameter typing, defaulting to "any". IDEs have correct TS definitions for .bind().