In a large bowl, whisk eggs then slowly add melted butter. Continue whisking until mixture thickens, then add milk and yogurt and mix until incorporated. Slowly add the dry mix and whisk until smooth.
Place the blackberries, sugar and cornstarch in a sauce pot and bring to a simmer over medium speed. Simmer 5 minutes then crush the berries with the back of a wooden spoon and remove from heat.
In a medium sized bowl using an electric hand blender, mix together the ricotta, cream cheese, sugar and lemon zest. Beat until smooth, then set aside.
Heat a large nonstick skillet or griddle to medium heat and pour 1/2 cup of the batter onto the hot surface. Using a spatula, spread the batter evenly to create an 8 inch pancake. Cook for 1-2 minutes, until the batter begins to bubble, then flip and cook a minute more on the second side.
Repeat with remaining batter, then spoon 1/4 cup of the ricotta filling down the middle of each pancake. Roll each blintz up and over the filling like a burrito, tucking in the edges as you roll. Pour blackberry sauce over each blintz and garnish with powdered sugar.