Boolean operations are a convenient way to transform geometry, but they can leave behind other problems. In this case you've generated a big and ugly n-gon (a polygon with more than 4 vertices). Ngons are notorious for deforming in unpredictable or undesirable ways. In general is preferable to work with quads.
Start by getting rid of the ngon
select the edge loop by pressing Alt while slecting an edge.
Press the space bar and type grid fill (or press CtrlF and select grid fill)
And play with the grid fill settings until you get something that does look like a grid.