A la Parilla This page first published: Jun 5, 2005 · Updated: Jun 24, 2018 · by CooksInfo. Copyright © 2021 · This post may contain affiliate links · This blog generates income via ads · “A La Parilla” is a Spanish cooking term. It means grilled or char-broiled so that the food has grate lines in it. Language Notes “Parilla” means “grill” in Spanish.