To make the syrup, add the kokutou, granulated sugar and water to a pot and bring to a simmer while stirring. It will tend to boil over, so don't let it out of your sight. If it's starts to boil over, just temporarily remove it from the heat. Keep stirring and watching until all the sugar has dissolved. Remove from the heat and then strain through a fine mesh strainer into a container.
Pass the all-purpose flour, matcha, granulated sugar, baking powder, baking soda and salt through a strainer and then whisk together to combine.
Melt the butter in the microwave until barely melted (but not boiling hot). If your butter is hot, let it a cool a bit before proceeding to the next step.
Whisk the egg into the butter and then whisk the butter mixture into the milk and yogurt until evenly combined.
Pour the wet ingredients into the dry ingredients and gently fold together until there are no large clumps of flour left (small clumps are okay). Do not overmix or pancakes will become tough.
If you have an electric griddle set it to 340 degrees F (170 C). Otherwise heat a large non-stick frying pan or griddle over medium heat until hot, but not sizzling hot.
Pour a bit of vegetable oil onto a paper towel and then use it to lightly oil the pan. Keep the paper towel to re-oil the pan periodically.
Pour the pancake batter into rounds onto the pan. The more you pour, the larger the pancakes will be. Let these cook until the edges start to dry out (are no longer glossy) and you start seeing bubbles come up in the middle of the pancake. Flip and cook the other side until cooked through.
I like to have my diners sitting at the table ready to eat so I can serve them straight from the pan, but if you want to sit down together, you can keep the matcha pancakes warm on a plate in a low temperature oven, covered with aluminum foil, until you've finished all the batter.