Prepare the dough. Heat the milk in the microwave in 15-second increments or on the stove until it's just warm to the touch. A thermometer should read around 110°F-115°F.
Stir in the yeast and 1 tablespoon of the sugar. Loosely cover with plastic wrap and let it stand for 5 minutes until it gets very foamy. If the mixture doesn't get foamy, throw it out and start again with a new packet of yeast.
In the bowl of a stand mixer (or a regular large bowl), whisk together 3 ½ cups of all-purpose flour, the remaining sugar, and salt.
Attach the dough hook to the mixer and add the melted butter, eggs, and yeast mixture. Mix together on medium-low speed for 6-8 minutes (or mix by hand), until the dough becomes smooth and elastic. The dough will be slightly tacky but not completely sticky. If it is still fairly sticky, knead in 1 tablespoon of additional flour at a time until smooth and elastic.
Coat a large bowl with oil and transfer the dough to the bowl, shaping it into a ball. Cover it with a kitchen towel and let it rise for 1 ½ to 2 hours, or until doubled in size.
Line 2 large baking sheets with parchment paper and set aside.
Divide the dough into 12 equal pieces and shape into balls. Place 6 balls on each of the prepared baking sheets and cover them loosely with clean kitchen towels. Let the balls rise again for 1 ½ hours in a warm place, or until doubled in size. While the conchas rise, make the topping.
Prepare the topping. Beat together the flour, powdered sugar, butter, maple extract, vanilla extract, and ground cinnamon in a large mixing bowl with a handheld mixer until it starts to clump together and resembles wet sand. Transfer the mixture to a clean surface and knead it with your hands until it forms a smooth paste.
Divide the mixture into 12 equal pieces and shape them into balls.
Lightly flatten each ball in between two sheets of parchment paper using a tortilla press or rolling pin.
Assemble the conchas. Drape the topping onto the risen concha dough. Lightly pat it down on the sides to secure the topping.
Preheat the oven to 350°F. While the oven is preheating, cut grooves into the topping using a paring knife to resemble a clamshell, a crisscross pattern, or whichever pattern you prefer. Be careful not to cut too deep and accidentally cut the concha dough.
Bake for 20 to 25 minutes, or until the bottom of the conchas is golden brown. Allow to cool for 5 minutes before slicing in half, horizontally.
Make the sandwiches. In a large skillet over medium heat, add the slices of bacon and cook until crispy on both sides. Transfer it to a plate lined with paper towels to drain.
In a separate large nonstick skillet, heat the olive oil over medium-high heat. Crack the eggs into the skillet and cook until the egg whites are just set, but the yolks are still runny. Gently flip over and cook for about 10-20 seconds. Set aside on a large plate.
Assemble the sandwiches by layering each concha bun with a slice of bacon, a fried egg, a few slices of avocado, and a sprinkle of cotija cheese.
Notes
Maple extract: While it gives these conchas a sweet flavor and aroma, you can omit it if you don’t have any in your pantry and just use all vanilla extract instead.