Preheat your oven to 375 F. Make sure you have a rack in the top third of your oven, at least 6 inches from the heat source. Line several baking sheets with parchment paper.
In a large bowl, mix your melted/browned butter, oil, and brown and white sugars until nice and smooth. Add the eggs + vanilla and mix until everything is well blended.
In a small bowl whisk together the bread flour, all-purpose flour, cinnamon, baking powder, baking soda, sea salt and nutmeg. Dump the flour mixture into the butter mixture and mix until the cookie dough is barely blended….you’ll still see streaks of flour. Add your oatmeal and finish mixing with just a few strokes. Lay some plastic wrap on the counter and dump the dough on top. Wrap tightly and stick in the fridge for at least 30 minutes…it will make it easier to work with.
Once the dough is chilled, gently roll into balls of about 3 tablespoons each and allow 2 inches of space between the balls on the prepared baking sheets. Press the dough down a bit so that they are like discs. Bake the cookies in the top third of the oven for 10 minutes. Allow to cool on the baking sheet for 5 minutes and then move to a cooling rack to finish cooling down.
Line a casserole dish with parchment or plastic wrap and scoop slightly softened ice cream into the dish, about ½ inch thick. Smooth over the top with a spatula and freeze for 20 minutes. Use a biscuit cutter or a drinking glass to cut out rounds of ice cream. Pick a glass or cookie cutter that is about the same size as the cookies. Press the ice cream rounds between two cookies and freeze the cookie sandwiches for 30 minutes.
While those freeze, heat up your cream (without bringing it to a boil) and pour over the chopped chocolate. Stir until smooth and cool. Add more cream in 1 tablespoon increments to thin if necessary. Cover another baking sheet with parchment paper. Dip half the frozen ice cream sandwich into the chocolate letting excess drip back into the bowl and set the sandwich on the parchment-covered baking sheet. Repeat with remaining sandwiches. Sprinkle with sea salt flakes if using. Freeze until ready to eat. If not eating immediately, once the sammies are frozen wrap each one tightly in plastic wrap and store in a freezer-safe, re-sealable plastic bag.