Preheat oven to 375 degrees F. Lightly spray a mini muffin pan with nonstick cooking spray.
In a large bowl, cream together the butter and white sugar until the mixture is light and fluffy, about a minute. Add the egg, and mix until well combined, about a minute. Stir in the flour and salt. Stir the baking soda into the yogurt, then add to the batter along with the lemon zest. Stir everything to combine, but do not over mix.
Spoon the muffin batter into the tin, filling the cups about 2/3 full.
Bake for 10 - 15 minutes, until the muffins are light golden brown.
Meanwhile, mix together the brown sugar and the meyer lemon juice, until the brown sugar is dissolved.
Remove the muffins from the oven, and drizzle the glaze over the warm muffins. Remove the muffins from the pan while they are still warm, and enjoy!