Preheat oven to 350°F / 175°C. Line loaf pan(s) with parchment.
Whisk together dry ingredients: flour, cornstarch, salt, baking powder, baking soda.
In stand mixer, beat butter and oil and sugar until light and fluffy.
Add eggs one at a time.
Mix in yogurt, buttermilk, vanilla bean paste, and lavender extract.
Turn off stand mixer. Add dry ingredients and mix by hand until just combined. Do not overmix.
Divide batter into two bowls. To earl grey bowl, add bloomed earl grey tea and extra vanilla bean paste.
Layer and swirl batters in pan(s).
Bake until golden and set, testing with a toothpick for doneness.
Cool completely before frosting.
For buttercream: Beat softened butter until pale and fluffy (2–3 minutes).
Add powdered sugar in 2 additions, mixing on low until smooth.
Mix in vanilla bean paste, lavender extract, and heavy cream.
Whip on medium-high speed until light and airy.
Frost cooled loaf with buttercream.
