Put a 3" wide board* of the correct length ("depth") onto 3" wide legs of the correct height to hold the top board up. Put a board at the bottom too, for stability. i e make a skinny table box then finish as desired (paint, contact paper, laminate of your choice, an exotic wood* with the proper finish, etc). If you move the stove as necessary, you could use 2x4 (finished 3.25 - 3.5" or so, wide) pieces for an exact fit with appropriate strength.
If you want the filler table to stay ( " " ) attached to the counter, consider using a double sided tape; unless you very sparingly use a glue that you can undo if you buy a larger stove in the future. No idea what that glue would be.
Doweling connecting countertop and add-on board seems a bit much; but done right you could skip the legs (a good glue job), and store a cutting board in the gap (or keep the legs, to block the visual hole.) Cut on a table saw to get straight and true cuts, for best finish joints.
====== *Like oak, alder, black walnut,,,, for the top board. Nails or screws go down.
[..........]
[..........] legs
[..........] with the dots as placeholders in my picture
====== bottom board, with nails going up, so not seen from front.