In a medium bowl, whisk together the flour, sugar, cinnamon, baking powder, baking soda, and kosher salt. Make sure to break up any lumps in the baking soda and distribute the cinnamon evenly throughout the dry mixture. Set this bowl aside—you'll use it in just a moment.
In a separate bowl, whisk together the oil, room-temperature buttermilk, vanilla extract, and egg until well combined. While the wet mixture sits for just a moment, start the peach filling in a saucepan: combine the sliced peaches, brown sugar, cinnamon, nutmeg, cornstarch, salt, and orange juice. Bring this to a boil over medium-high heat, stirring occasionally so the cornstarch dissolves and the filling begins to thicken. I like to let the peaches cook for about 5 minutes until the sauce becomes glossy and thick—this concentrates the fruit flavor beautifully.
Pour the wet ingredient mixture into the bowl with the dry ingredients and gently fold together using a spatula or wooden spoon—don't overmix. The batter should be slightly lumpy; overmixing develops too much gluten and makes pancakes tough. Let the batter rest for 10 minutes at room temperature; this allows the flour to fully hydrate and the leavening agents to activate, resulting in fluffier pancakes.
Heat a large skillet or griddle over medium heat and lightly butter it. Once hot, pour 1/4 cup of batter per pancake onto the cooking surface, leaving space between them. Cook for about 3 minutes until the edges look set and bubbles form on the surface, then flip and cook for another 1.5 minutes until golden brown on the second side. I find that medium heat gives the best results—hot enough to create a golden exterior but slow enough that the inside cooks through without burning. Transfer cooked pancakes to a warm plate and repeat with remaining batter.
By now, your peach filling from Step 2 should be thick and glossy. Give the peach filling one final stir and check the consistency—if it seems too runny, let it simmer another minute or two. Stack the warm pancakes on serving plates, spoon the peach compote generously over the top, and drizzle with maple syrup. Finish with a dollop of whipped cream or a scoop of vanilla ice cream for that classic cobbler experience.