Whisk flour, salt, and baking soda together in medium bowl; set aside.
Melt butter in a pan over medium-high heat, swirling pan occasionally, until foaming subsides. Continue to cook, stirring and scraping bottom of pan with heat-resistant spatula, until milk solids are dark golden brown and butter has nutty aroma, 1 to 2 minutes. Immediately transfer browned butter to large heatproof bowl, scraping skillet with spatula. Stir in cinnamon.
Add brown sugar, granulated sugar, and oil to bowl with butter and whisk until combined.
Add eggs, vanilla and orange zest and whisk until mixture is smooth. Make sure browned butter mixture has cooled enough before adding eggs.
Stir in flour mixture until fully combined, about 1 minute.
Add oats and cranberries and stir until evenly distributed (mixture will be stiff). Cover dough with plastic wrap and chill for a couple of hours in the refrigerator.
Adjust oven rack to middle position and preheat oven to 375 degrees. Line 2 rimmed baking sheets with parchment paper. Using a #20 cookie scoop, scoop out dough and place dough balls 2 inches apart on prepared sheets. Using back of measuring cup sprayed with nonstick spray, press each ball into a disk.
Top with cookie with sprinkling of Demerara or sparkling sugar if desired before baking.
Bake, 1 sheet at a time, until cookie edges are set and lightly browned and centers are still soft but not wet, 8 to 10 minutes, rotating sheet halfway through baking. Let cookies cool on sheet on wire rack for 5 minutes; transfer cookies to wire rack and let cool completely. Store in airtight container.