In a large pot of boiling, salted water, cook the noodles according to package directions; drain, then press into a greased 9-inch pie pan. Let cool slightly.
Meanwhile, in a medium bowl, stir together the hoisin, 1/2 cup pineapple juice, 2 tablespoons oil and the crushed red pepper.
In a large nonstick skillet, heat 3 tablespoons oil over medium heat. Slide the noodle cake into the pan and cook until deep golden underneath, about 5 minutes. Carefully flip the noodle cake and cook until browned underneath, about 5 minutes.
In a large skillet, heat 1 tablespoon oil over high heat. Add the pineapple chunks and green beans and cook, stirring occasionally, until the pineapple is browned and the beans begin to blister, 2 to 3 minutes; transfer to a plate. Add the remaining 1 tablespoon oil, the shrimp and garlic to the pan and cook for 1 minute. Stir in the hoisin mixture and the reserved pineapple and green beans, lower the heat to low and cook until the shrimp are opaque, about 2 minutes. Spoon the shrimp mixture on top of the crispy noodle cake and serve immediately.