For the basic buttermilk pancakes: Whisk together the flour, sugar, baking powder, baking soda and salt in a large bowl.
Whisk together the eggs until smooth, whisk in the buttermilk and vanilla until smooth. Add the wet to the dry along with the butter and the optional ingredients, if using, and mix until just combined. (Lumps are ok). Let sit at room temperature for at least 15 minutes and up to 30 minutes before using.
Preheat the oven to 200 degrees F. Heat a griddle, nonstick pan or cast iron pan over medium heat until evenly heated, about 5 minutes. Brush with butter and add a few teaspoons of oil.
Drop scant 1/4 cups of the batter onto the griddle or into the pan and cook until the bottom of the pancakes are golden brown and the top surface becomes slightly dry and bubbles begin to form, about 3 minutes. Carefully flip over using a fish spatula or metal spatula and cook until the other side is lightly golden brown, about 2 minutes longer. Serve immediately slathered with the butter and drizzled with the syrup…or transfer to baking sheets in even layers and keep warm in oven.
For the blackberry-blueberry butter (compound butter): Combine the berries, sugar and 1/4 cup of water in a medium saucepan and bring to a boil over high heat. Cook until the berries break down and the mixture thickens, about 15 minutes. Add the lemon juice and transfer to a bowl to cool. This mixture can be made 3 days in advance and can be stored, covered, in a bowl in the refrigerator.
For a chunky butter: Combine the fruit, butter and salt in a bowl and mix until combined. For a smooth butter, combine the fruit, butter and salt in the bowl of a food processor and process until smooth.
Serve at room temperature or scrape into a bowl, cover and refrigerate for up to 5 days or freeze up to a month.
For the maple-cinnamon syrup (flavored syrups): Combine the syrup, cinnamon and salt in a small saucepan and bring to a boil over high heat. Remove, cover with a lid and let steep for at least 1 hour. Can be made 3 days in advance and stored covered in the refrigerator. Bring to a simmer before serving and remove and discard cinnamon sticks.