Preheat the oven to 375 degrees F. Spray mini muffin tins with nonstick spray.
Cream together the butter and granulated sugar in a large bowl by hand or using an electric mixer. Add the eggs and beat well. Mix in the flour. In a separate bowl, dissolve the baking soda in the buttermilk. Add the buttermilk mixture to the batter along with the orange zest and mix well.
Fill the muffin tins two-thirds full with the batter and bake until lightly browned, 12 to 17 minutes.
In a separate bowl, combine the brown sugar and orange juice (you should have about 1/2 cup juice) and mix well. Drizzle this glaze over the warm muffins in the tins. Remove the muffins while still warm.
If you don't have buttermilk, add 1 tablespoon white vinegar to just under 1 cup of milk.