Inadequately described.

What other info would be helpful?

Might be a Spanish Elder, Piper swartzianum

Flowers white and the leaves have a pepper taste.

Ian

As for other info that is generally needed for id: shape, texture, size of the leaf; how the leaf is arranged (alternate or opposite on the branch); the shape of the flowers; any other distinguishing characteristics (like striped bark, flakey bark, berries).

And a picture is always helpful.

first thought based on the brief description is clethra alnifolia. some part of the plant is peppery-tasting.
should not be in flower now, though.

Here is a link that might be useful: sweet pepperbush, clethra

The leaves are broad (not needle- or scale-like).

The petioles have an alternate arrangement.

The leaves compound (multiple leaves arise from each petiole).

The petioles are spaced about 1/2 inch along the stem.

The stems have a rough (scaly) surface.

The leaves have a smooth margin.

The leaves have pinnate (not parallel) veins.

The leaf's midpoint is wider than its base and apex.

The leaf has a fairy rough (not smooth) texture.

The leaf has a dull (not shiny) surface.

It's not a clethra alnifolia.

My plant is not deciduous and the leaves are not dark-green and glossy. (They are dull and are light green).

The white flowers do not grow in spikes (racemes). Although the shrub is not blooming now, the flowers grown singly. I recall (I think) that the flowers are daisy- or star-shaped.

I guess the closest FAQ would be this partly relevant one.

Here is a link that might be useful: How can I identify a found/unknown/mystery rose?

My shrub is a broadleaf (not deciduous).

All of the stems are light green and they have a bumpy surface (similar to scales on a fish or shingles on a roof).

The petioles have an alternate arrangement and are spaced about every 1/2 inch along the stem.

The leaves are compound (multiple leaves arise from along the petiole), have a linear shape (the midpoint is wider than its base and its apex), have pinnate venation, have smooth margins, have a light green color, have a dull surface and feel somewhat leathery.

The white star-shaped (?) flowers are single flowers (they do not grown in spikes (racemes).

.
. My plant is an Artemisia dracunculus (a.k.a. wormwood; French tarragon)