Procedure:

1) Heat oven to 350 F. Place the pitted, stemmed cherries, and their juices, in a small saucepan with the sugar. Bring to a boil, stirring until sugar is melted, then reduce heat to a moderate simmer. When juice has reduced by 1/2 - about 15 minutes - remove from heat and add the almond extract. Transfer to a small bowl and refrigerate.

2) As cherries simmer, measure half the buckwheat groats and all the walnut pieces into a spice or coffee grinder. Pulse and steady-grind until a fine flour forms. Transfer to a medium bowl, using a butter knife to scrape the slightly moist flour from the bottom of the grinder. Grind the second half of the groats to a fine flour and add to the bowl. Add the salt and the baking powder and stir well to mix..

3) Grease the bottom and sides of the cake pan with butter and line with parchment. Grease the bottom parchment. Quarter the peaches and slice into pieces about 1/2 inch thick, arranging on the cake pan bottom. (see photo, below). 

4) Put the butter into a medium bowl. Mix on medium speed to cream butter until light and fluffy, about  3 minutes. Add the sugars and cream again. Add the eggs, one at a time, mixing on low speed until just incorporated. Add the vanilla extract and mix until just incorporated. Fold in the flour and the sweetened cherries in four passes: half the flour, then half the cherries, then the rest of the flour, then the rest of the cherries. Pour batter into the prepared cake pan and place on a middle rack in the oven.

5) Bake 40 - 45 minutes, until an inserted toothpick comes out clean. Cool on a rack for about 1/2 hour, then invert over a plate or serving dish. Remove cake pan and parchment. Serve slightly warm if possible.

Yes you can serve it with ice cream.