For the cake: Preheat oven to 350° F. Butter and flour a 10-inch, 12 cup bundt pan and set aside.
In the bowl of a stand mixer with a paddle attachment, whip together the butter and sugar until pale yellow and fluffy. Add the eggs, one at a time, until smooth. All of this should take about 7 minutes.
In a separate bowl, whisk together the flour, salt, and baking powder. In a separate cup, mix together the cherry puree, oil, and vanilla.
With the mixer on the lowest speed, alternate adding the dry ingredients and the cherry mixture. Increase speed to medium for about 30 seconds until the batter is smooth. Fold in the chopped cherries.
Pour into prepared pan, smoothing out the top. Bake at 350 for 50-60 minutes, until the top is set and crackly and a tester comes out clean.
Let cool for about 10 minutes in the pan, then invert onto a rack and let cool completely before glazing, about 2 hours.
For the glaze: In a stand mixer fitted with the paddle attachment, beat butter and cream cheese on medium speed for about 30 seconds, until smooth and uniform.
Add confectioner's sugar, salt, and vanilla and beat on low speed for about 30 seconds to combine. With the mixer running on low, slowly stream in the cherry puree, a bit at a time, until you reach the right consistency. Pourable, but not too runny.
To glaze, place cake on rack on a parchment-lined baking sheet. I transfered the glaze to a 2 cup pyrex liquid measuring cup and poured it slowly around the top, letting it drip into the cake grooves. The baking sheet will catch any drips and the parchment makes cleaning it all up quick and easy.
For the fresh cherry puree
Place all ingredients in a food processor and blend on high until smooth. Makes about 2 cups.