For the muffins, combine 2 cups flour, sugar, baking powder and salt in a large bowl. Make a well in the center.
Mix the yogurt, the oil, the eggs and lemon juice. Add to dry ingredients and stir until blended.
In a small bowl, toss together the apples, brown sugar, cinnamon, and vanilla. Fold apples into the batter. Using a large cookie scoop, fill a greased muffin pan about ⅔ full.
Bake at 375 for 20-25 minutes or until golden brown. Remove muffins from pan and let cool on a wire rack.
To prepare the glaze, melt butter in a saucepan over medium heat. Add brown sugar and heavy cream, stir until sugar has dissolved and the mixture combines. Remove from heat and whisk in powdered sugar until creamy and smooth. Allow caramel glaze to cool slightly. When ready, dip muffin tops into glaze and place on a baking rack to set.