Preheat oven to 350 degrees. Grease and line a 13 x 9 pan with parchment. Leave some overhang on parchment paper--this will help with removing brownies from pan.
Melt butter and chocolate in double boiler until fully melted and smooth, and let cool slightly. In a stand mixer with a whisk attachment, beat chocolate mixture on low, and add sugar. Beat until sugar is fully incorporated.
Turn speed up on mixer to medium, and add the eggs one-by-one, being sure to beat each egg into batter until fully incorporated. Stop to scrape bowl with rubber spatula to insure all ingredients are blended well. Turn on mixer to medium-high, and beat for one minute, and add in vanilla extract.
In a separate bowl, sift together gluten-free flour, cocoa powder, salt, espresso powder, and cinnamon. With mixer on low setting, add dry ingredients to batter, beat until incorporated. Stop mixer to scrape bowl, then beat batter on medium for 1 minute.
Pour batter into prepared pan, and bake for 45-50 minutes, until an inserted toothpick comes out with a few moist crumbs.
Cool pan fully (about 2 hours), then chill in refrigerator for at least 2 hours. Turn brownies out of pan, then cut into pieces. Store in airtight container.