Heat the oven to 450F. Roast the cherries whole (with their pits) on a parchment lined baking sheet for 40 minutes, stirring once halfway through cooking.
When the cherries have cooled enough to handle, pit them, reserving pits and juices (use gloves for this unless you want to have cherry-juice stained hands.)
Transfer the pits to a small pot and set aside. Transfer the cherries and their juices to a food processor and puree until smooth. Pour the cherry puree into a large bowl and set aside.
Add the cream, milk, sugar, and salt to the pot with the cherry pits, and bring to a simmer over medium-low heat. Stir until the sugar dissolves, about 5 minutes. Reduce heat to very low, and let stand 10 minutes more to infuse the flavor from the cherry pits. Remove from heat.
Meanwhile, whisk the egg yolks in a medium bowl for 1 minute until well combined and slightly lighter in color. Slowly whisk 1/3 of the hot cream and cherry pit mixture into the yolks, then whisk the entire yolk mixture back into the pot with the cream mixture. (This will temper the yolks and keep them from curdling, so really whisk briskly here!)
Return the pot to medium-low heat, and bring the cream base to 170F while whisking constantly. The mixture will slightly thicken, and should coat the back of a spoon when 170F is reached.
Strain the cream base through a fine mesh sieve into the bowl with the pureed cherries and discard the pits. Stir to combine, and allow to sit 10 minutes at room temperature to infuse. Strain the mixture through a fine mesh sieve or cheesecloth into a clean bowl and cool to room temperature. When cooled, cover and chill in the refrigerator at least 4 hours or overnight.