Beat 1 cup unsalted butter, softened, for 20 seconds in a large bowl with electric beaters or a stand mixer.
Add 1 cup white granulated sugar gradually while you continue beating at medium speed, and then for 3 more minutes after adding all of it. The mixture will be light in color, fluffy, and the sugar will have partially dissolved.
Add 4 eggs, one at a time, beating well after each addition. Make sure to scrape the sides of the bowl regularly.
Add 1 ½ teaspoons pure vanilla extract with 1 teaspoon orange zest and mix.
Sift the dry ingredients (2 ¼ cups all-purpose or cake flour, 1 teaspoon baking powder and ¼ teaspoon salt) together in a bowl, or have them measured and sift them directly over the egg-sugar batter.
Add them in 2 parts, alternating with ¼ cup cream cheese in 1 part. That means you start and end with the dry ingredients. Mix and integrate it well, but don't beat it much at this point. After adding the flour cake batter should be beaten *just* until fully incorporated, but no more.
Add the fresh strawberry pieces and integrate them with a spatula. Just a few strokes, trying not to crush them much, or at all.
Put the thick batter in the prepared pan and smooth the top.
Bake for about 45 minutes, until it rises, the top cracks, and a cake tester or toothpick inserted in the middle comes out clean. Pound cakes are dense, so make sure it's fully baked. If the top is browning too quickly, but the middle is not done, cover it loosely with a piece of foil and continue to bake.
Cool on a wire rack and remove carefully from the pan, removing the strip of paper.
Drizzle the glaze over and let it dry before cutting. Serve with some extra fresh strawberries if you want.