Heat milk, sugar, and salt in a medium saucepan over medium heat. Stir constantly, until the mixture just reaches the point of simmer. Remove from heat.
In a separate medium heat-proof bowl, lightly whisk egg yolks. Pour about half of the warm milk into the bowl with the egg yolks, whisking while you do so. Pour the egg/milk mixture back into the saucepan with the rest of the milk.
Cook mixture over low heat, stirring constantly, until it thickens enough to coat the back of the spoon (or reaches a temperature of about 170 degrees).
Pour the heavy cream into a separate large bowl. Strain the egg/milk mixture into the heavy cream and stir to combine. Stir in whole jelly beans. I chose to use pink, orange, and red jelly beans so the mixture would turn a nice color, but you can use the colors of your choice. Cover bowl with plastic wrap and place in the fridge for at least 4 hours.
Once mixture has been sufficiently chilled, process in ice cream maker according to manufacturer’s directions. When the ice cream is almost done hardening, mix in the chopped jelly beans.
Scoop ice cream in airtight containers and place in the freezer for another 4+ hours, but ideally overnight.
Scoop into bowls and enjoy. Note that the jelly beans in the ice cream get a little hard in the freezer, so take care when biting into them.