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Preheat the oven to 375°F. Line a muffin pan with papers, and grease the papers.
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Measure the flour by gently spooning it into a cup, then sweeping off any excess. In a medium-sized bowl, whisk together the flour, baking powder, baking soda, and salt, then set aside.
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In a large bowl, beat the butter or vegetable oil and sugar with a hand-held or stand mixer, until light and fluffy. Start the mixer at low speed until the ingredients are incorporated, then gradually increase speed to medium-high. If using butter, the mixture should turn almost white in color; if using oil, the mixture should look frothy.
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Scrape down the bowl to make sure all the butter or oil is incorporated, then add the eggs one at a time, beating well after each addition.
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Add the vanilla and sour cream or yogurt, and mix until incorporated.
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Add the dry ingredients and mix on low speed just until the batter is smooth. The batter will be very thick, almost like cookie dough.
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Fold in the berries by hand. If you use frozen berries, the batter will become even stiffer; don't worry about it, it's fine.
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Scoop the batter into the prepared muffin cups, using a heaping 1/4-cup for each. Again, the batter will be thick and stiff; don't expect it to settle. Sprinkle with regular granulated or coarse white sugar, if desired.
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Bake the muffins for 18 to 24 minutes, until a cake tester inserted in the center of one comes out clean.
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Remove them from the oven, and take them out of the baking pan as soon as you can and transfer to a rack to finish cooling. (Leaving hot muffins in the pan creates steam that will toughen the muffins as they sit.)
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Store leftovers for a couple of days at room temperature in an airtight container, or freeze for up to 1 month.
