It seems to me that you are asking about a haircut that is colloquially referred to in the Yeshivah world as having a "tshup" (I believe the term comes from Yiddish by way of Russian чуб). Many of the later Aharonim/Poseqim use the term בלורית to describe this haircut, however they are not using it in the technical sense in which it originally refers to a forbidden heathen haircut (the Tosefta Shabboth 7:1 deems a בלורית darkhei ha-Emori, the ways of the Emorites).
There is a debate about what exactly the classical בלורית consists of (see Rashi on Sotah 49b and Rambam, H. AZ 11:1, and Beth Yosef YD 178 for different interpretations of the Rambam). However what is contemporarily known as a בלורית does not satisfy these positions. Rabbi Yaaqov Sasson (following the rulings of his grandfather R. Obhadia Yosef) clarifies (האם מותר לגדל בלורית):
אין איסור בגידול הבלורית באופן שמגדל קצת שיער לצד הפנים. (שנקרא
בזמנינו "בלורית"). ואין איסור בגידול בלורית כפי שנוהגים בזמנינו, משום
שאין זה בגדר חוקות הגויים.
There is no prohibition in growing a בלורית in a manner wherein the hair on the sides is grown shorter (which is called in our times
"בלורית"). And there is no prohibition on growing a בלורית in the
manner that people are accustomed to in our day, since this does not
fall within the purview of following gentile ways.
The Aharonim/Poseqim that criticize the contemporary בלורית (aka a "tshup") primarily condemn it on two grounds: 1) That it is a conceited hairstyle, and 2) its effects on the proper donning of tefillin.
For example, the Mishnah Berurah 27:15 states:
כתב בספר מחצית השקל ורע עלי המעשה של אותן האנשים שמגדלין בלורותיהן
מלבד כי הוא דרך שחץ וגאוה עיין מה שכתוב ביו"ד סימן קע"ו יש בו איסור
בהנחת תפילין דכיון דגדולין הרבה ליכא למימר בהו היינו רביתייהו וחוצצים
עי"ש ובלאו חציצה נמי בשביל הני שערות המרובים א"א לצמצם שיהיו מהודקין
ומונחין על מקומן כדין
In the work Mahasith ha-Sheqel, the author writes "I am vexed by the
conduct of those people who allow their forelocks (בלורותיהן) to grow. Apart from
the fact that this is haughty and arrogant behavior (see YD 176), it
also involves the transgression of a prohibition, when one dons
tefillin. For in view of the fact that the locks of the hair are very
long, one cannot argue that they constitute normal growth and they are
therefore ruled as an interposition between the tefillin unit and the
flesh." See there. Actually this practice would also be objectionable
without the question of the interposition. For because of those
numerous hairs it is impossible to adjust the position of the tefillin
with exactitude so that they will be tightly donned in their proper
place, in accordance with halakhic requirements.
As far as the first concern comes into play, this is more in the realm of middoth than outright din per se, and accordingly some take a more lenient tact whilst cautioning against growing the hair too long and/or being preoccupied with looks. On the issue of an interposition between the tefillin and the head, the Arukh ha-Shulhan takes the position that even long hair in its own natural place is not a problem of interposition, however where a בלורית is grown such that its hair encircles/envelops the hair of another area of the head then it would be a problem (AH 27:15):
ויש רוצים להחמיר גם כשהשיער גדול מאוד. ואיני רואה בזה שום טעם, דאיזה
גבול תתן להשיער? ושיער הראש כעצם הראש דמי. ואולי אם יש לו בלורית שמסבב
גם צדדי השיער של מקום אחר למקום הנחת תפילין – בזה וודאי יש חציצה, אבל
לא השיער הטבעי הגדל במקום זה. וכן המנהג פשוט, ואין לפקפק כלל בזה
This perspective seems to allow for a minor/moderate "tshup" provided that it doesn't fall subject to the aforementioned consideration.