Preheat the oven to 350°F (175°C).
Line an 8 1/2 x 4 1/2-inch loaf pan with parchment paper, leaving enough overhang to lift the bread from the pan.
In a large bowl, whisk together the flour, baking powder, baking soda, and salt until evenly combined.
In a separate bowl, whisk the egg, granulated sugar, brown sugar, and buttermilk until smooth.
Add the oil and vanilla extract to the wet ingredients and whisk until completely combined.
Pour the wet ingredients into the dry ingredients. Gently mix just until no large pockets of flour remain.Do not overmix.
Add the fresh raspberries and gently fold them into the batter, taking care not to crush them.
Pour the batter into the prepared loaf pan and spread it evenly.
Place the loaf pan on a baking sheet and loosely cover the top with aluminum foil. Bake for approximately 1 hour.
Remove the foil near the end of baking and continue baking uncovered until the top is lightly golden. Check the center with a toothpick. It should come out clean or with a few moist crumbs but no wet batter.
Allow the bread to cool in the pan for about 15 minutes. Lift it from the pan and transfer it to a wire rack to cool completely.
To make the icing, whisk the powdered sugar, heavy cream, and vanilla extract until smooth. If necessary, add a few drops of heavy cream to reach your desired consistency.
Drizzle the vanilla icing over the completely cooled raspberry bread. Let the icing set before slicing and serving.