Prep your peaches by cutting them in half and removing the pits.
Poach the peaches: Add the water, granulated sugar, cardamom pods, and cinnamon stick to a medium-sized pot. Stir the liquid over medium-high heat until the sugar dissolves into the water. Let the liquid come to a simmer and place the peach halves into the poaching liquid. Cover the pot and let the peaches poach for 5 to 6 minutes. Flip the peaches over with some tongs, cover the pot again, and let them continue to poach for an additional 5 to 6 minutes. You will know that the peaches are done when they are easily pierced by a fork or knife. Take the pot off of the heat, add in the vanilla extract and stir to incorporate. Transfer the peaches along with the poaching liquid to a bowl and let them cool in your fridge for at least 1 hour.
(Optional) Use your hands to peel the skin off of the poached peaches once they have cooled completely.
Make the raspberry sauce: Add the raspberries to either a blender or food processor and pulse until it forms a smooth puree. Strain the puree through a fine mesh sieve over a medium-sized mixing bowl. Add in a ⅛ cup of powdered sugar and whisk until it is fully incorporated into the raspberry puree. Keep adding in a little bit of the powdered sugar and whisking it into the puree until the entire 1 cup of powdered sugar is fully incorporated. Place the raspberry sauce into your fridge and let it cool for an hour.
Assemble the peach melba: Add a couple of scoops of the vanilla ice cream into a small serving dish. Place 1 of the poached peach halves over the scoops of ice cream, and drizzle some of the raspberry sauce over top. Sprinkle on some of the slivered almonds as a garnish if using.
Serve immediately and enjoy.