How to Make It
Preheat broiler to high with oven rack 6 inches from heat. Cut kernels from corn cobs to equal about 2 cups; reserve cobs. Toss together kernels, canola oil, and 3/4 teaspoon salt on a rimmed baking sheet until kernels are well coated. Spread into a single layer, and broil in preheated oven until beginning to char, 4 to 6 minutes. Set aside.
Using the back of a knife, scrape milk from corn cobs into a small saucepan. Add corn cobs and 1 cup whole milk. Bring to a simmer over medium-low, and cook, stirring occasionally, 5 minutes. Remove from heat. Let stand at room temperature 30 minutes.
Pour milk mixture through a fine wire-mesh strainer into a bowl. Scrape cooked cobs with a spoon to release milk; discard cobs and other solids. Add 1 1/2 cups heavy cream and 1/4 teaspoon salt to bowl. Transfer milk mixture to saucepan, and bring to a simmer over medium-low. Meanwhile, whisk together egg yolks, 1/2 cup sugar, and 1/2 teaspoon vanilla in a medium bowl. Gradually add two-thirds of the simmering milk mixture to egg yolk mixture, whisking constantly, until incorporated.
Stir egg yolk–milk mixture into remaining milk mixture in saucepan. Reduce heat to low, and cook, stirring constantly, until mixture thickens and coats the back of a spoon, about 12 minutes. Transfer crème anglaise to a medium bowl, and stir in lime zest. Press plastic wrap directly on surface, and cool completely, about 2 hours. Set aside. (Cooled crème anglaise can be chilled up to 1 day. To reheat, transfer to a small saucepan, and heat over low, stirring constantly, until just warm, 2 to 3 minutes.)
Preheat oven to 325°F. Whisk together eggs, bourbon, remaining 1 cup heavy cream, remaining 1 cup milk, remaining 1/4 cup sugar, remaining 1 teaspoon vanilla, and remaining 1/4 teaspoon salt in a medium bowl. Toss together croissants, French bread, and roasted corn in a large bowl. Add bourbon-cream mixture to bread mixture, and stir to combine. Let stand at room temperature 30 to 45 minutes, stirring occasionally.
Pour bread mixture into a lightly greased 9-inch square baking pan, and spread in an even layer. Bake at 325°F until set and lightly browned, 35 to 40 minutes. Transfer pan to a wire rack, and let cool 30 minutes before slicing. Cut bread pudding into squares; serve with crème anglaise, and garnish with caramel popcorn.