Preheat and prepare pan. Position a rack in the center of the oven. Preheat oven to 350°F (180°C). Grease a 9x13 cake pan.
Make filling. In a small bowl, beat together the very soft butter, salt, brown sugar, cinnamon and flour until a soft wet paste forms. Set aside. 12 Tablespoons (1 ½ sticks, 170 g) unsalted butter ¼ teaspoon salt 1 cup (213 g) packed light brown sugar 1 ½ tablespoons ground cinnamon 2 Tablespoons all purpose flour
Combine dry ingredients. In a mixing bowl, whisk together flour, baking powder, and salt. Set aside. 3 ¼ cups (390 g) all purpose flour 1 tablespoon baking powder 1 teaspoon salt
Cream butter oil and sugar. In a second mixing bowl with an electric mixer on medium speed, cream butter, oil and sugar together until smooth and combined about 2 to 3 minutes. ½ cup (1 stick, 113 g) unsalted butter, ½ cup (120 mL) canola oil (or vegetable) 2 cups (400 g) granulated white sugar
Add eggs, vanilla. Add the eggs one at a time, beating well after each addition. Scrape down the sides and bottom of the bowl after each addition. Add vanilla extract. Beat to combine. 4 large eggs 1 tablespoon vanilla extract
Alternate dry ingredients with buttermilk. Alternate adding the flour mixture with the buttermilk, beginning and ending with the flour mixture. Do not overmix. Stop mixing once the last of the flour has been mixed in. I like to give the last few stirs with a spatula to ensure it's not overmixed. 1 ½ cups (360 mL) buttermilk
Bake. Spread the batter in the pan. Dollop the cinnamon mixture on top in small teaspoon amounts (do not do big dollops or they have a tendency to sink to the bottom). Swirl with the tip of the knife. Bake for about 35-40 minutes. The cake is done when it's golden brown on top and toothpick inserted into the center comes out clean or with a few moist crumbs. Remove cake from the oven.
Make glaze. In a small bowl, whisk together glaze ingredients. Spread glaze over a slightly warm cake. Slice and serve. 2 cups (226 g) powdered sugar 2 Tablespoons (28 g) unsalted butter ½ teaspoon vanilla extract 3-4 Tablespoon milk