Place the croissants on two parchment-lined baking sheets, leaving at least 1 inch of space between each. Set aside.
Preheat the oven to 375 F.
Prepare the cookie dough: In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugars to combine.
Add the egg and vanilla and beat until smooth.
Add 1 ⅔ cups flour, the salt, baking powder, and baking soda. Beat just until no dry ingredients are visible.
Add ¾ cup mini chocolate chips and beat lightly to combine.
Prepare the crumble: In a small bowl, use your fingertips to mix ½ cup of the prepared cookie dough with the remaining ¼ cup flour and the walnuts, if using, to form even crumbs. Set aside.
Use a spoon to spread about 2 tablespoons of the remaining cookie dough into the center of each croissant.
Spread the remaining cookie dough over the top of each to act as glue for the crumble.
Top the croissants evenly with crumble, pressing to adhere.
Bake for 20 to 22 minutes, until the tops are golden brown.
Melt the remaining ¼ cup chocolate chips with the vegetable oil in a microwave or double boiler.
Drizzle the melted chocolate over the baked crookies.
Serve immediately, dusted with confectioners' sugar and sprinkled with flaky sea salt, if desired.