Measure and cut eight pieces, each 34-1/2 inches long, from your 2-by-4-inch poplar.
Double your pieces to create four 4-by-4-inch table legs. Apply a thin layer of wood glue to the surfaces to be joined and attach them with 2 1/4-inch trim head screws. Allow glue to set.
Measure 6 inches up from the bottom of each table leg. Measure and chisel a 1-1/2-inch notch on the inside face of each leg. This will provide a means of support for a shelf to be built next.
Measure and cut two 2-by-3-inch pieces of poplar to a length of 43 inches, and two 2-by-3-inch pieces to 34 inches. These pieces will frame the table's shelf.
Place the short ends between the longer sides. Apply wood glue to the faces to be joined. Drive 3 1/2-inch trim-head screws through the longer sides and into the shorter ends. Allow to set.
Measure, cut and attach equally spaced 2-by-2-inch crosspieces into the frame. Glue and screw each crosspiece using 3 1/2-inch trim-head screws driven through the frame and into the ends of the crosspiece.
Apply glue to the leg notches and corners of the shelf and secure the shelf to the legs with 2 1/2-inch trim-head screws driven through the outside of the leg and into the shelf.
Measure and cut two 2-by-6-inch pieces of poplar to 40 inches and two to 27 inches. These pieces will form the apron that sits between the table legs.
Shave a slice off the top corner of each leg to allow it to rest snugly against your surface-mounted corner brackets. Attach the corner brackets to join your table legs to the apron.
Fill the screw holes and the seams between the 2-by-4s that form the legs using a putty knife and wood filler. Allow to dry. Prime and paint the table frame.
Measure, cut and screw three 31-inch crosspieces on the flat, flush with the top and between the long sides of the apron. Use 2 1/4-inch trim head screws for this.
Fit your drill/driver with the 1/2-inch bit. Drill two holes in each 1-by-3-inch crosspiece.
Apply a bead of silicone caulk to the top edge of the apron and to the crosspieces. Center the butcher block on the table frame.
Drive a 2-inch deck screw fitted with a 1-inch fender washer up through each hole drilled into the 1-by-3-inch crosspiece and into the bottom of the butcher block. These screws will hold the block in place and prevent warping of the wood.