This right?

web.php

<?php
Route::group(['prefix' => 'ead'], function () {
    Route::resource('', 'ead\EadProjectController');
    Route::resource('/{ead}/parts', 'ead\EadPartController');
    Route::group(['prefix' => 'admin'], function () {
        Route::get('/', 'ead\EadProjectController@admin');
        Route::resource('msl', 'EadMSLCodeController');
        Route::resource('placement', 'EadPartPlacementController');
        Route::resource('category', 'EadPartCategoryController');
    });
});

Route::get('/', 'HomeController@index');

// Commented out so that Achievo/ATK can handle the authentication required.
// Auth::routes();