Using a sharp knife, cut chicken in half through thickest side parallel to cutting board. Place pieces between 2 pieces of plastic wrap or in a large resealable bag on a large cutting board. Using a meat mallet or rolling pin, pound chicken to ¼" thick.
In a large bowl, combine coconut milk, lime juice, and fish sauce. Add chicken and toss to combine. Cover bowl and refrigerate at least 30 minutes and up to 1 hour.
In a large shallow bowl, whisk flour, cornstarch, salt, and a few grinds of pepper. In a second shallow bowl, beat eggs to blend. In a third shallow bowl, stir panko and coconut.
Working one at a time, remove chicken from marinade and toss in flour mixture. Dip into eggs, letting excess drip off, then coat in panko mixture, gently pressing to adhere.
Into a large, stainless steel skillet, pour oil to a depth of ½". Heat over medium-high heat until shimmering but not smoking (oil temperature should be around 350°). Working in batches if needed, carefully add chicken and cook, turning halfway through, until deeply golden brown, 3 to 4 minutes per side. Transfer to a wire rack. Repeat with remaining chicken, adjusting heat as needed.