To me those holes look like something you would see in an incense holder. I used to have one made of terra cotta that looked like an adobe house, that I purchased on my very first trip to Santa Fe, New Mexico.
I did a quick google search to see if I could find a picture of one like the one that I used to have, and instead I stumbled across the Incense Burner Virtual Museum website (http://www.kandaki.com/BP-Index.php?st=c&shp=Building). The one I used to have was similar to the fifth one down on the linked page.
But, looking at the other items on the page, there were two that specifically reminded me of your item:
and this one:
The Incense Burner Virtual Museum site describes the usages for each one--the top one is designed for use with a scented pastille, and the bottom one is supposed to be used with perfumed oil.
With that information, my next search took me to this Pinterest page called "Pastille Burners," which states that these items were "quite popular in aristocratic homes during the reign of Queen Elizabeth I." Make sure to go take a look at the page (https://www.pinterest.com/tlight2/pastille-burners/); many of the pieces shown remind me of yours.