Whisk the egg white in a shallow bowl until it looks foamy, then combine the nut flour, Parmesan, garlic powder, salt, and pepper in a second shallow bowl. The egg white should be lightly frothy, and the dry coating should look evenly seasoned with no clumps.

Dry the chicken tenders thoroughly, coat each one first in egg white and then in the flour mixture, and arrange them on a wax paper-lined plate. Press the coating on gently so it adheres without becoming packed or pasty.

Heat 1 1/2 tablespoons olive oil with 1/2 tablespoon butter in a large skillet over medium heat, then sear half of the chicken for about 3 minutes per side before transferring it to a plate. The cutlets should release readily and show a deep golden crust rather than pale, damp patches.

Add another 1 1/2 tablespoons olive oil and 1/2 tablespoon butter, then cook the remaining chicken in the same way. Keep space between the pieces so the skillet stays hot enough to brown the coating.

Cook the shallot and garlic in the skillet for about 30 seconds, then pour in the chicken broth and add the lemon slices. When the shallot and garlic smell sweet and fragrant, add the liquid before they begin to darken.

Bring the broth mixture to a simmer and cook until it has reduced by half, about 7 minutes. The sauce should look slightly fuller and leave a brief trail when stirred across the skillet.

Stir in the lemon juice and capers, then remove the skillet from the heat and blend in the remaining butter in 3 pieces until smooth; whisk in ¼ teaspoon glucomannan or xanthan gum if a thicker sauce is desired, then season with salt and pepper. Add each piece of butter only after the previous one has melted, creating a glossy sauce rather than an oily layer.

Arrange the chicken over lightly steamed zucchini noodles or cauliflower rice and spoon the sauce over just before serving. Serve promptly so the coating keeps its crisp edges beneath the warm lemon-caper sauce.