Arrange a rack in center of oven; preheat to 400°. Line a 17" x 11" or 16" x 12" baking sheet with foil; grease foil with cooking spray. Arrange crackers in a single layer on prepared sheet, covering the foil from edge to edge and trimming crackers to fit as needed.
In a medium pot over medium heat, cook butter and brown sugar, stirring with a heatproof rubber spatula, until butter is melted. (If mixture starts to boil before butter is melted, reduce heat to medium-low and stir vigorously, mashing down on butter to encourage it to melt as quickly as possible.) When butter is melted, bring mixture to a boil over medium-high heat. Cook, undisturbed, 3 minutes.
Pour toffee over crackers, using an offset metal spatula or the back of heatproof rubber spatula to spread toffee across entire cracker layer.
Bake toffee until bubbly and light caramel in color, 5 to 7 minutes. Remove from oven. Let sit until bubbles subside, about 1 minute.
Sprinkle chips over top. Continue to bake until chips are melted, about 1 minute more.
Using offset spatula, gently spread chocolate into a smooth, even layer. Sprinkle with sea salt (if using). Let sit at room temperature until cooled, about 30 minutes. Refrigerate until firm, about 90 minutes.