Preheat the oven to 350 degrees. Brush the top of a muffin pan with vegetable oil and line it with 12 paper liners.
Stir together the flour, salt, baking powder, baking soda, and cinnamon in a medium bowl. In a large bowl, whisk together the yogurt, sugar, 1/2 cup vegetable oil, honey, eggs, and vanilla until combined. Add the dry ingredients, stirring just until combined. Gently stir in the wheat bran and blueberries until combined.
Scoop the batter into the muffin cups with a rounded 2 1/4-inch ice cream scoop. Bake for 25 to 30 minutes, until the tops are golden brown and a cake tester comes out clean. Allow to cool for 5 minutes and serve warm or at room temperature.