Is this problem more likely to happen the colder the weather?
I can't remember the name for it but it's common with flues.
A pocket of cold air is forming inside the flue. The relatively cold early-fire smoke cannot penetrate it. You need to generate a fast blast of hot air to punch a hole thru that cold pocket.
Before you light the fire, light a sheet of newspaper and hold it near the top of the stove/fireplace. You need a good flame so make sure you haven't the newspaper balled up. With a bit of trial and error you'll figure out how many sheets of newspaper you'll need. One usually suffices for me.
Another problem can relate to disparity in air pressure. Open the window for a few minutes.
I don't know much about cowls though some can be quite aesthetic.