Preheat oven to 350 degrees and generously butter a pie plate.
If your peach slices are super juicy, pat them with paper towels to eliminate some of the moisture. Put the slices in a large bowl with lemon juice and 1 tablespoon flour in a bowl and toss to combine.
In a large bowl, whisk together eggs, sugar, vanilla extract, cardamom (or cinnamon), and salt until combined and frothy.
Whisk in the remaining ½ cup flour until just combined. Add heavy cream and whole milk to the bowl and whisk until smooth.
Arrange peaches in prepared pie dish. I layer them over each other several times, making sure not to pack them too tightly, so batter can get through. You can reserve a few to place on top of batter.
Pour batter over peaches. Some will likely rise up.
Bake clafoutis for 45-55 minutes, until the custard is puffed, golden around the edges, and just set in the center. A knife inserted about 2 inches from the center should come out mostly clean and the center should jiggle slightly, but not look wet. Note: If your peaches are extra juicy or you're using a deep baking dish, your clafoutis may take up to 65 minutes to fully set. Keep an eye on it and loosely tent with foil if the top starts to brown too quickly.
Let clafoutis cool for at least 20 minutes, so custard can set.
Dust your peach clafoutis with confectioners' sugar before serving.