Preheat oven to 375 degrees F. Line a muffin pan with liners.
Make espresso streusel. Melt butter in a saute pan over medium-low heat until browned. Let cool and stir in instant coffee. Add brown sugar, cinnamon, and rye flour until combined. The streusel will be crumbly.
Prepare muffin batter. Dissolve instant coffee in milk. Whisk milk mixture with melted butter, yogurt, vanilla, and egg.
Combine all-purpose flour with rye flour, sugar, baking powder, cinnamon, and salt. Add wet ingredients and stir just until combined. Stir in chocolate chips.
Fill prepared pan with muffin batter and sprinkle coffee streusel on top. Bake for 18-22 minutes or until a toothpick inserted in the center comes out clean. Remove the muffins from the pan and cool completely on a wire rack.
Meanwhile, make coffee glaze. Dissolve instant coffee with water. Pour coffee mixture into powdered sugar and mix until well combined. Drizzle coffee glaze on the espresso rye chocolate chip muffins.