Most robotic hands and grippers rely on actuators with large gearboxes and force sensors for controlling gripping force. However, this might not be ideal for tasks that require the robot to interact with an unstructured and unknown environment. In this paper, we introduce a novel quasi-direct-drive two-fingered robotic hand with variable impedance control in the joint space and Cartesian space. The hand has a total of four degrees of freedom, backdrivable differential gear trains, and four brushless direct current (BLDC) motors. Motor torque is controlled through Field-Oriented Control (FOC) with current sensing. Variable impedance control enables the robotic hand to execute dexterous manipulation tasks safely during environment-robot and human-robot interactions. The quasi-direct-drive actuators eliminate the need for complex tactile/force sensors or precise motion planning when handling environmental contact. A majority-3D-printed assembly makes this a low-cost research platform built with affordable, readily available off-the-shelf components. Experimental validation demonstrates the robotic hand's capability for stable force-closure and form-closure grasps in the presence of disturbances, reliable in-hand manipulation, and safe dynamic manipulations despite contact with the environment.