In a large bowl, whisk together flour, sugar, baking powder, and salt.
Add milk, cream, and vanilla syrup to a large jar and shake well to combine (if you don't have a jar, you can stir together in a bowl).
In a small bowl, lightly whisk eggs.
Add sweet cream mixture and whisked eggs to the dry ingredients and stir until they’re just combined, taking care not to over-mix. Some lumps are OK. Let batter rest for 5-10 minutes.
Heat a griddle or skillet over medium heat and brush lightly with a little butter or cooking spray. Pour about ⅓ cup of batter onto it. Cook for about 2 minutes, until bubbles start to form on the surface and then flip and cook for another minute, until golden brown.
Serve pancakes with sweet cream foam (see notes) or whipped cream and maple syrup.